Chapter 23: One-Step and Two-Step Equations
Learn Grade 7 mathematics from very beginner explanations through worked examples, practice, reasoning, and review.
Chapter Overview
This chapter teaches One-Step and Two-Step Equations with simple language, step-by-step reasoning, and original worked examples. Technical words are explained in plain language.
Key Technical Terms
- Rational Number (a number that can be written as a fraction of integers with a nonzero denominator)
- Prime Number (a whole number greater than 1 with exactly two positive factors)
- Ratio (a comparison of two quantities)
- Equation (a statement that two expressions are equal)
- Estimate (a close approximation used to check whether an answer is reasonable)
- Solution (a value or result that satisfies the problem)
- Representation (a way to show mathematics using symbols, diagrams, tables, graphs, or words)
- Reasonableness (whether an answer makes sense in the context of the problem)
How to Learn This Chapter
Read the explanation first, follow the examples one step at a time, cover the answer and retry the problem yourself, then use the practice and review questions to check understanding.
23.1 Meaning of equation
An equation says that two expressions are equal. This topic focuses on Meaning of equation .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Solve 2x+5=3x-1.
- Simplify each side if needed.
- Collect variable terms on one side.
- Collect constants on the other side.
- Divide to isolate the variable.
- Check by substitution.
Very beginner explanation: An equation says that two expressions are equal. This topic focuses on Meaning of equation .
Answer: x=6
Worked Example 2
Problem: Solve 4x-7=13.
- Simplify each side if needed.
- Collect variable terms on one side.
- Collect constants on the other side.
- Divide to isolate the variable.
- Check by substitution.
Very beginner explanation: An equation says that two expressions are equal. This topic focuses on Meaning of equation .
Answer: x=5
Worked Example 3
Problem: Solve 3x+2=2x+9.
- Simplify each side if needed.
- Collect variable terms on one side.
- Collect constants on the other side.
- Divide to isolate the variable.
- Check by substitution.
Very beginner explanation: An equation says that two expressions are equal. This topic focuses on Meaning of equation .
Answer: x=7
Worked Example 4
Problem: Solve 5x+4=2x+19.
- Simplify each side if needed.
- Collect variable terms on one side.
- Collect constants on the other side.
- Divide to isolate the variable.
- Check by substitution.
Very beginner explanation: An equation says that two expressions are equal. This topic focuses on Meaning of equation .
Answer: x=5
Worked Example 5
Problem: Solve 2(x+3)=18.
- Simplify each side if needed.
- Collect variable terms on one side.
- Collect constants on the other side.
- Divide to isolate the variable.
- Check by substitution.
Very beginner explanation: An equation says that two expressions are equal. This topic focuses on Meaning of equation .
Answer: x=6
Worked Example 6
Problem: Solve 2x + 5 = 17.
- Simplify each side if needed.
- Use inverse operations to collect variable terms and constants.
- Keep both sides balanced.
- Check by substitution.
Very beginner explanation: An equation stays balanced when equivalent operations are applied correctly.
Answer: x = 6
Worked Example 7
Problem: Solve 3x - 4 = 11.
- Simplify each side if needed.
- Use inverse operations to collect variable terms and constants.
- Keep both sides balanced.
- Check by substitution.
Very beginner explanation: An equation stays balanced when equivalent operations are applied correctly.
Answer: x = 5
Worked Example 8
Problem: Solve 5x + 7 = 2x + 22.
- Simplify each side if needed.
- Use inverse operations to collect variable terms and constants.
- Keep both sides balanced.
- Check by substitution.
Very beginner explanation: An equation stays balanced when equivalent operations are applied correctly.
Answer: x = 5
Worked Example 9
Problem: Solve 4(x + 2) = 24.
- Simplify each side if needed.
- Use inverse operations to collect variable terms and constants.
- Keep both sides balanced.
- Check by substitution.
Very beginner explanation: An equation stays balanced when equivalent operations are applied correctly.
Answer: x = 4
Worked Example 10
Problem: Solve 7x - 3 = 4x + 12.
- Simplify each side if needed.
- Use inverse operations to collect variable terms and constants.
- Keep both sides balanced.
- Check by substitution.
Very beginner explanation: An equation stays balanced when equivalent operations are applied correctly.
Answer: x = 5
Practice Exercise
Create one new question about Meaning of equation. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
23.2 Equality
Equality is an important Grade 7 idea in One-Step and Two-Step Equations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Equality: Identify a correct example.
- State the definition and show why the example fits.
- Show all important reasoning.
Very beginner explanation: Equality is an important Grade 7 idea in One-Step and Two-Step Equations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 2
Problem: Equality: Identify a non-example.
- Explain which requirement is missing.
- Show all important reasoning.
Very beginner explanation: Equality is an important Grade 7 idea in One-Step and Two-Step Equations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 3
Problem: Equality: Compare two cases.
- State one similarity and one difference.
- Show all important reasoning.
Very beginner explanation: Equality is an important Grade 7 idea in One-Step and Two-Step Equations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 4
Problem: Equality: Apply the idea in a real situation.
- Translate the situation into mathematical language.
- Show all important reasoning.
Very beginner explanation: Equality is an important Grade 7 idea in One-Step and Two-Step Equations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 5
Problem: Equality: Create and check your own example.
- Use the definition, then verify each condition.
- Show all important reasoning.
Very beginner explanation: Equality is an important Grade 7 idea in One-Step and Two-Step Equations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 6
Problem: Solve 2x + 5 = 17.
- Simplify each side if needed.
- Use inverse operations to collect variable terms and constants.
- Keep both sides balanced.
- Check by substitution.
Very beginner explanation: An equation stays balanced when equivalent operations are applied correctly.
Answer: x = 6
Worked Example 7
Problem: Solve 3x - 4 = 11.
- Simplify each side if needed.
- Use inverse operations to collect variable terms and constants.
- Keep both sides balanced.
- Check by substitution.
Very beginner explanation: An equation stays balanced when equivalent operations are applied correctly.
Answer: x = 5
Worked Example 8
Problem: Solve 5x + 7 = 2x + 22.
- Simplify each side if needed.
- Use inverse operations to collect variable terms and constants.
- Keep both sides balanced.
- Check by substitution.
Very beginner explanation: An equation stays balanced when equivalent operations are applied correctly.
Answer: x = 5
Worked Example 9
Problem: Solve 4(x + 2) = 24.
- Simplify each side if needed.
- Use inverse operations to collect variable terms and constants.
- Keep both sides balanced.
- Check by substitution.
Very beginner explanation: An equation stays balanced when equivalent operations are applied correctly.
Answer: x = 4
Worked Example 10
Problem: Solve 7x - 3 = 4x + 12.
- Simplify each side if needed.
- Use inverse operations to collect variable terms and constants.
- Keep both sides balanced.
- Check by substitution.
Very beginner explanation: An equation stays balanced when equivalent operations are applied correctly.
Answer: x = 5
Practice Exercise
Create one new question about Equality. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
23.3 Inverse operations
A ratio compares two quantities in a fixed order. This topic focuses on Inverse operations .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Calculate 12 × 8.
- Use a known fact, distributive strategy, or standard multiplication.
- Check using division: 96 ÷ 8 = 12.
Very beginner explanation: A ratio compares two quantities in a fixed order. This topic focuses on Inverse operations .
Answer: 96
Worked Example 2
Problem: Calculate 9 × 7.
- Use a known fact, distributive strategy, or standard multiplication.
- Check using division: 63 ÷ 7 = 9.
Very beginner explanation: A ratio compares two quantities in a fixed order. This topic focuses on Inverse operations .
Answer: 63
Worked Example 3
Problem: Calculate 144 × 12.
- Use a known fact, distributive strategy, or standard multiplication.
- Check using division: 1728 ÷ 12 = 144.
Very beginner explanation: A ratio compares two quantities in a fixed order. This topic focuses on Inverse operations .
Answer: 1728
Worked Example 4
Problem: Calculate 325 × 6.
- Use a known fact, distributive strategy, or standard multiplication.
- Check using division: 1950 ÷ 6 = 325.
Very beginner explanation: A ratio compares two quantities in a fixed order. This topic focuses on Inverse operations .
Answer: 1950
Worked Example 5
Problem: Calculate 728 × 8.
- Use a known fact, distributive strategy, or standard multiplication.
- Check using division: 5824 ÷ 8 = 728.
Very beginner explanation: A ratio compares two quantities in a fixed order. This topic focuses on Inverse operations .
Answer: 5824
Worked Example 6
Problem: Simplify the ratio 4:6.
- Find the greatest common factor, 2.
- Divide both terms by 2.
Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both quantities by the same common factor.
Answer: 2:3
Worked Example 7
Problem: Simplify the ratio 8:12.
- Find the greatest common factor, 4.
- Divide both terms by 4.
Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both quantities by the same common factor.
Answer: 2:3
Worked Example 8
Problem: Simplify the ratio 15:25.
- Find the greatest common factor, 5.
- Divide both terms by 5.
Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both quantities by the same common factor.
Answer: 3:5
Worked Example 9
Problem: Simplify the ratio 18:30.
- Find the greatest common factor, 6.
- Divide both terms by 6.
Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both quantities by the same common factor.
Answer: 3:5
Worked Example 10
Problem: Simplify the ratio 21:28.
- Find the greatest common factor, 7.
- Divide both terms by 7.
Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both quantities by the same common factor.
Answer: 3:4
Practice Exercise
Create one new question about Inverse operations. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
23.4 Addition equations
An equation says that two expressions are equal. This topic focuses on Addition equations .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Solve 2x+5=3x-1.
- Simplify each side if needed.
- Collect variable terms on one side.
- Collect constants on the other side.
- Divide to isolate the variable.
- Check by substitution.
Very beginner explanation: An equation says that two expressions are equal. This topic focuses on Addition equations .
Answer: x=6
Worked Example 2
Problem: Solve 4x-7=13.
- Simplify each side if needed.
- Collect variable terms on one side.
- Collect constants on the other side.
- Divide to isolate the variable.
- Check by substitution.
Very beginner explanation: An equation says that two expressions are equal. This topic focuses on Addition equations .
Answer: x=5
Worked Example 3
Problem: Solve 3x+2=2x+9.
- Simplify each side if needed.
- Collect variable terms on one side.
- Collect constants on the other side.
- Divide to isolate the variable.
- Check by substitution.
Very beginner explanation: An equation says that two expressions are equal. This topic focuses on Addition equations .
Answer: x=7
Worked Example 4
Problem: Solve 5x+4=2x+19.
- Simplify each side if needed.
- Collect variable terms on one side.
- Collect constants on the other side.
- Divide to isolate the variable.
- Check by substitution.
Very beginner explanation: An equation says that two expressions are equal. This topic focuses on Addition equations .
Answer: x=5
Worked Example 5
Problem: Solve 2(x+3)=18.
- Simplify each side if needed.
- Collect variable terms on one side.
- Collect constants on the other side.
- Divide to isolate the variable.
- Check by substitution.
Very beginner explanation: An equation says that two expressions are equal. This topic focuses on Addition equations .
Answer: x=6
Worked Example 6
Problem: Solve 2x + 5 = 17.
- Simplify each side if needed.
- Use inverse operations to collect variable terms and constants.
- Keep both sides balanced.
- Check by substitution.
Very beginner explanation: An equation stays balanced when equivalent operations are applied correctly.
Answer: x = 6
Worked Example 7
Problem: Solve 3x - 4 = 11.
- Simplify each side if needed.
- Use inverse operations to collect variable terms and constants.
- Keep both sides balanced.
- Check by substitution.
Very beginner explanation: An equation stays balanced when equivalent operations are applied correctly.
Answer: x = 5
Worked Example 8
Problem: Solve 5x + 7 = 2x + 22.
- Simplify each side if needed.
- Use inverse operations to collect variable terms and constants.
- Keep both sides balanced.
- Check by substitution.
Very beginner explanation: An equation stays balanced when equivalent operations are applied correctly.
Answer: x = 5
Worked Example 9
Problem: Solve 4(x + 2) = 24.
- Simplify each side if needed.
- Use inverse operations to collect variable terms and constants.
- Keep both sides balanced.
- Check by substitution.
Very beginner explanation: An equation stays balanced when equivalent operations are applied correctly.
Answer: x = 4
Worked Example 10
Problem: Solve 7x - 3 = 4x + 12.
- Simplify each side if needed.
- Use inverse operations to collect variable terms and constants.
- Keep both sides balanced.
- Check by substitution.
Very beginner explanation: An equation stays balanced when equivalent operations are applied correctly.
Answer: x = 5
Practice Exercise
Create one new question about Addition equations. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
23.5 Subtraction equations
An equation says that two expressions are equal. This topic focuses on Subtraction equations .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Solve 2x+5=3x-1.
- Simplify each side if needed.
- Collect variable terms on one side.
- Collect constants on the other side.
- Divide to isolate the variable.
- Check by substitution.
Very beginner explanation: An equation says that two expressions are equal. This topic focuses on Subtraction equations .
Answer: x=6
Worked Example 2
Problem: Solve 4x-7=13.
- Simplify each side if needed.
- Collect variable terms on one side.
- Collect constants on the other side.
- Divide to isolate the variable.
- Check by substitution.
Very beginner explanation: An equation says that two expressions are equal. This topic focuses on Subtraction equations .
Answer: x=5
Worked Example 3
Problem: Solve 3x+2=2x+9.
- Simplify each side if needed.
- Collect variable terms on one side.
- Collect constants on the other side.
- Divide to isolate the variable.
- Check by substitution.
Very beginner explanation: An equation says that two expressions are equal. This topic focuses on Subtraction equations .
Answer: x=7
Worked Example 4
Problem: Solve 5x+4=2x+19.
- Simplify each side if needed.
- Collect variable terms on one side.
- Collect constants on the other side.
- Divide to isolate the variable.
- Check by substitution.
Very beginner explanation: An equation says that two expressions are equal. This topic focuses on Subtraction equations .
Answer: x=5
Worked Example 5
Problem: Solve 2(x+3)=18.
- Simplify each side if needed.
- Collect variable terms on one side.
- Collect constants on the other side.
- Divide to isolate the variable.
- Check by substitution.
Very beginner explanation: An equation says that two expressions are equal. This topic focuses on Subtraction equations .
Answer: x=6
Worked Example 6
Problem: Solve 2x + 5 = 17.
- Simplify each side if needed.
- Use inverse operations to collect variable terms and constants.
- Keep both sides balanced.
- Check by substitution.
Very beginner explanation: An equation stays balanced when equivalent operations are applied correctly.
Answer: x = 6
Worked Example 7
Problem: Solve 3x - 4 = 11.
- Simplify each side if needed.
- Use inverse operations to collect variable terms and constants.
- Keep both sides balanced.
- Check by substitution.
Very beginner explanation: An equation stays balanced when equivalent operations are applied correctly.
Answer: x = 5
Worked Example 8
Problem: Solve 5x + 7 = 2x + 22.
- Simplify each side if needed.
- Use inverse operations to collect variable terms and constants.
- Keep both sides balanced.
- Check by substitution.
Very beginner explanation: An equation stays balanced when equivalent operations are applied correctly.
Answer: x = 5
Worked Example 9
Problem: Solve 4(x + 2) = 24.
- Simplify each side if needed.
- Use inverse operations to collect variable terms and constants.
- Keep both sides balanced.
- Check by substitution.
Very beginner explanation: An equation stays balanced when equivalent operations are applied correctly.
Answer: x = 4
Worked Example 10
Problem: Solve 7x - 3 = 4x + 12.
- Simplify each side if needed.
- Use inverse operations to collect variable terms and constants.
- Keep both sides balanced.
- Check by substitution.
Very beginner explanation: An equation stays balanced when equivalent operations are applied correctly.
Answer: x = 5
Practice Exercise
Create one new question about Subtraction equations. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
23.6 Multiplication equations
A tip is an extra amount, often calculated as a percent of a bill. This topic focuses on Multiplication equations .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Find 10% of $80.
- Convert 10% to 0.1.
- Multiply by 80.
Very beginner explanation: A tip is an extra amount, often calculated as a percent of a bill. This topic focuses on Multiplication equations .
Answer: $8.00
Worked Example 2
Problem: Find 25% of $60.
- Convert 25% to 0.25.
- Multiply by 60.
Very beginner explanation: A tip is an extra amount, often calculated as a percent of a bill. This topic focuses on Multiplication equations .
Answer: $15.00
Worked Example 3
Problem: Find 15% of $120.
- Convert 15% to 0.15.
- Multiply by 120.
Very beginner explanation: A tip is an extra amount, often calculated as a percent of a bill. This topic focuses on Multiplication equations .
Answer: $18.00
Worked Example 4
Problem: Find 5% of $250.
- Convert 5% to 0.05.
- Multiply by 250.
Very beginner explanation: A tip is an extra amount, often calculated as a percent of a bill. This topic focuses on Multiplication equations .
Answer: $12.50
Worked Example 5
Problem: Find 13% of $75.
- Convert 13% to 0.13.
- Multiply by 75.
Very beginner explanation: A tip is an extra amount, often calculated as a percent of a bill. This topic focuses on Multiplication equations .
Answer: $9.75
Worked Example 6
Problem: Find 10% of $90.
- Convert 10% to 0.1.
- Multiply by 90.
Very beginner explanation: Percent of an amount is found by multiplying the amount by the percent written as a decimal.
Answer: $9.00
Worked Example 7
Problem: Find 25% of $64.
- Convert 25% to 0.25.
- Multiply by 64.
Very beginner explanation: Percent of an amount is found by multiplying the amount by the percent written as a decimal.
Answer: $16.00
Worked Example 8
Problem: Find 15% of $140.
- Convert 15% to 0.15.
- Multiply by 140.
Very beginner explanation: Percent of an amount is found by multiplying the amount by the percent written as a decimal.
Answer: $21.00
Worked Example 9
Problem: Find 5% of $260.
- Convert 5% to 0.05.
- Multiply by 260.
Very beginner explanation: Percent of an amount is found by multiplying the amount by the percent written as a decimal.
Answer: $13.00
Worked Example 10
Problem: Find 20% of $75.
- Convert 20% to 0.2.
- Multiply by 75.
Very beginner explanation: Percent of an amount is found by multiplying the amount by the percent written as a decimal.
Answer: $15.00
Practice Exercise
Create one new question about Multiplication equations. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
23.7 Division equations
An equation says that two expressions are equal. This topic focuses on Division equations .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Solve 2x+5=3x-1.
- Simplify each side if needed.
- Collect variable terms on one side.
- Collect constants on the other side.
- Divide to isolate the variable.
- Check by substitution.
Very beginner explanation: An equation says that two expressions are equal. This topic focuses on Division equations .
Answer: x=6
Worked Example 2
Problem: Solve 4x-7=13.
- Simplify each side if needed.
- Collect variable terms on one side.
- Collect constants on the other side.
- Divide to isolate the variable.
- Check by substitution.
Very beginner explanation: An equation says that two expressions are equal. This topic focuses on Division equations .
Answer: x=5
Worked Example 3
Problem: Solve 3x+2=2x+9.
- Simplify each side if needed.
- Collect variable terms on one side.
- Collect constants on the other side.
- Divide to isolate the variable.
- Check by substitution.
Very beginner explanation: An equation says that two expressions are equal. This topic focuses on Division equations .
Answer: x=7
Worked Example 4
Problem: Solve 5x+4=2x+19.
- Simplify each side if needed.
- Collect variable terms on one side.
- Collect constants on the other side.
- Divide to isolate the variable.
- Check by substitution.
Very beginner explanation: An equation says that two expressions are equal. This topic focuses on Division equations .
Answer: x=5
Worked Example 5
Problem: Solve 2(x+3)=18.
- Simplify each side if needed.
- Collect variable terms on one side.
- Collect constants on the other side.
- Divide to isolate the variable.
- Check by substitution.
Very beginner explanation: An equation says that two expressions are equal. This topic focuses on Division equations .
Answer: x=6
Worked Example 6
Problem: Solve 2x + 5 = 17.
- Simplify each side if needed.
- Use inverse operations to collect variable terms and constants.
- Keep both sides balanced.
- Check by substitution.
Very beginner explanation: An equation stays balanced when equivalent operations are applied correctly.
Answer: x = 6
Worked Example 7
Problem: Solve 3x - 4 = 11.
- Simplify each side if needed.
- Use inverse operations to collect variable terms and constants.
- Keep both sides balanced.
- Check by substitution.
Very beginner explanation: An equation stays balanced when equivalent operations are applied correctly.
Answer: x = 5
Worked Example 8
Problem: Solve 5x + 7 = 2x + 22.
- Simplify each side if needed.
- Use inverse operations to collect variable terms and constants.
- Keep both sides balanced.
- Check by substitution.
Very beginner explanation: An equation stays balanced when equivalent operations are applied correctly.
Answer: x = 5
Worked Example 9
Problem: Solve 4(x + 2) = 24.
- Simplify each side if needed.
- Use inverse operations to collect variable terms and constants.
- Keep both sides balanced.
- Check by substitution.
Very beginner explanation: An equation stays balanced when equivalent operations are applied correctly.
Answer: x = 4
Worked Example 10
Problem: Solve 7x - 3 = 4x + 12.
- Simplify each side if needed.
- Use inverse operations to collect variable terms and constants.
- Keep both sides balanced.
- Check by substitution.
Very beginner explanation: An equation stays balanced when equivalent operations are applied correctly.
Answer: x = 5
Practice Exercise
Create one new question about Division equations. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
23.8 Balancing equations
An equation says that two expressions are equal. This topic focuses on Balancing equations .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Solve 2x+5=3x-1.
- Simplify each side if needed.
- Collect variable terms on one side.
- Collect constants on the other side.
- Divide to isolate the variable.
- Check by substitution.
Very beginner explanation: An equation says that two expressions are equal. This topic focuses on Balancing equations .
Answer: x=6
Worked Example 2
Problem: Solve 4x-7=13.
- Simplify each side if needed.
- Collect variable terms on one side.
- Collect constants on the other side.
- Divide to isolate the variable.
- Check by substitution.
Very beginner explanation: An equation says that two expressions are equal. This topic focuses on Balancing equations .
Answer: x=5
Worked Example 3
Problem: Solve 3x+2=2x+9.
- Simplify each side if needed.
- Collect variable terms on one side.
- Collect constants on the other side.
- Divide to isolate the variable.
- Check by substitution.
Very beginner explanation: An equation says that two expressions are equal. This topic focuses on Balancing equations .
Answer: x=7
Worked Example 4
Problem: Solve 5x+4=2x+19.
- Simplify each side if needed.
- Collect variable terms on one side.
- Collect constants on the other side.
- Divide to isolate the variable.
- Check by substitution.
Very beginner explanation: An equation says that two expressions are equal. This topic focuses on Balancing equations .
Answer: x=5
Worked Example 5
Problem: Solve 2(x+3)=18.
- Simplify each side if needed.
- Collect variable terms on one side.
- Collect constants on the other side.
- Divide to isolate the variable.
- Check by substitution.
Very beginner explanation: An equation says that two expressions are equal. This topic focuses on Balancing equations .
Answer: x=6
Worked Example 6
Problem: Solve 2x + 5 = 17.
- Simplify each side if needed.
- Use inverse operations to collect variable terms and constants.
- Keep both sides balanced.
- Check by substitution.
Very beginner explanation: An equation stays balanced when equivalent operations are applied correctly.
Answer: x = 6
Worked Example 7
Problem: Solve 3x - 4 = 11.
- Simplify each side if needed.
- Use inverse operations to collect variable terms and constants.
- Keep both sides balanced.
- Check by substitution.
Very beginner explanation: An equation stays balanced when equivalent operations are applied correctly.
Answer: x = 5
Worked Example 8
Problem: Solve 5x + 7 = 2x + 22.
- Simplify each side if needed.
- Use inverse operations to collect variable terms and constants.
- Keep both sides balanced.
- Check by substitution.
Very beginner explanation: An equation stays balanced when equivalent operations are applied correctly.
Answer: x = 5
Worked Example 9
Problem: Solve 4(x + 2) = 24.
- Simplify each side if needed.
- Use inverse operations to collect variable terms and constants.
- Keep both sides balanced.
- Check by substitution.
Very beginner explanation: An equation stays balanced when equivalent operations are applied correctly.
Answer: x = 4
Worked Example 10
Problem: Solve 7x - 3 = 4x + 12.
- Simplify each side if needed.
- Use inverse operations to collect variable terms and constants.
- Keep both sides balanced.
- Check by substitution.
Very beginner explanation: An equation stays balanced when equivalent operations are applied correctly.
Answer: x = 5
Practice Exercise
Create one new question about Balancing equations. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
23.9 Two-step equations
An equation says that two expressions are equal. This topic focuses on Two-step equations .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Solve 2x+5=3x-1.
- Simplify each side if needed.
- Collect variable terms on one side.
- Collect constants on the other side.
- Divide to isolate the variable.
- Check by substitution.
Very beginner explanation: An equation says that two expressions are equal. This topic focuses on Two-step equations .
Answer: x=6
Worked Example 2
Problem: Solve 4x-7=13.
- Simplify each side if needed.
- Collect variable terms on one side.
- Collect constants on the other side.
- Divide to isolate the variable.
- Check by substitution.
Very beginner explanation: An equation says that two expressions are equal. This topic focuses on Two-step equations .
Answer: x=5
Worked Example 3
Problem: Solve 3x+2=2x+9.
- Simplify each side if needed.
- Collect variable terms on one side.
- Collect constants on the other side.
- Divide to isolate the variable.
- Check by substitution.
Very beginner explanation: An equation says that two expressions are equal. This topic focuses on Two-step equations .
Answer: x=7
Worked Example 4
Problem: Solve 5x+4=2x+19.
- Simplify each side if needed.
- Collect variable terms on one side.
- Collect constants on the other side.
- Divide to isolate the variable.
- Check by substitution.
Very beginner explanation: An equation says that two expressions are equal. This topic focuses on Two-step equations .
Answer: x=5
Worked Example 5
Problem: Solve 2(x+3)=18.
- Simplify each side if needed.
- Collect variable terms on one side.
- Collect constants on the other side.
- Divide to isolate the variable.
- Check by substitution.
Very beginner explanation: An equation says that two expressions are equal. This topic focuses on Two-step equations .
Answer: x=6
Worked Example 6
Problem: Solve 2x + 5 = 17.
- Simplify each side if needed.
- Use inverse operations to collect variable terms and constants.
- Keep both sides balanced.
- Check by substitution.
Very beginner explanation: An equation stays balanced when equivalent operations are applied correctly.
Answer: x = 6
Worked Example 7
Problem: Solve 3x - 4 = 11.
- Simplify each side if needed.
- Use inverse operations to collect variable terms and constants.
- Keep both sides balanced.
- Check by substitution.
Very beginner explanation: An equation stays balanced when equivalent operations are applied correctly.
Answer: x = 5
Worked Example 8
Problem: Solve 5x + 7 = 2x + 22.
- Simplify each side if needed.
- Use inverse operations to collect variable terms and constants.
- Keep both sides balanced.
- Check by substitution.
Very beginner explanation: An equation stays balanced when equivalent operations are applied correctly.
Answer: x = 5
Worked Example 9
Problem: Solve 4(x + 2) = 24.
- Simplify each side if needed.
- Use inverse operations to collect variable terms and constants.
- Keep both sides balanced.
- Check by substitution.
Very beginner explanation: An equation stays balanced when equivalent operations are applied correctly.
Answer: x = 4
Worked Example 10
Problem: Solve 7x - 3 = 4x + 12.
- Simplify each side if needed.
- Use inverse operations to collect variable terms and constants.
- Keep both sides balanced.
- Check by substitution.
Very beginner explanation: An equation stays balanced when equivalent operations are applied correctly.
Answer: x = 5
Practice Exercise
Create one new question about Two-step equations. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
23.10 Equations with negative numbers
An equation says that two expressions are equal. This topic focuses on Equations with negative numbers .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Solve 2x+5=3x-1.
- Simplify each side if needed.
- Collect variable terms on one side.
- Collect constants on the other side.
- Divide to isolate the variable.
- Check by substitution.
Very beginner explanation: An equation says that two expressions are equal. This topic focuses on Equations with negative numbers .
Answer: x=6
Worked Example 2
Problem: Solve 4x-7=13.
- Simplify each side if needed.
- Collect variable terms on one side.
- Collect constants on the other side.
- Divide to isolate the variable.
- Check by substitution.
Very beginner explanation: An equation says that two expressions are equal. This topic focuses on Equations with negative numbers .
Answer: x=5
Worked Example 3
Problem: Solve 3x+2=2x+9.
- Simplify each side if needed.
- Collect variable terms on one side.
- Collect constants on the other side.
- Divide to isolate the variable.
- Check by substitution.
Very beginner explanation: An equation says that two expressions are equal. This topic focuses on Equations with negative numbers .
Answer: x=7
Worked Example 4
Problem: Solve 5x+4=2x+19.
- Simplify each side if needed.
- Collect variable terms on one side.
- Collect constants on the other side.
- Divide to isolate the variable.
- Check by substitution.
Very beginner explanation: An equation says that two expressions are equal. This topic focuses on Equations with negative numbers .
Answer: x=5
Worked Example 5
Problem: Solve 2(x+3)=18.
- Simplify each side if needed.
- Collect variable terms on one side.
- Collect constants on the other side.
- Divide to isolate the variable.
- Check by substitution.
Very beginner explanation: An equation says that two expressions are equal. This topic focuses on Equations with negative numbers .
Answer: x=6
Worked Example 6
Problem: Solve 2x + 5 = 17.
- Simplify each side if needed.
- Use inverse operations to collect variable terms and constants.
- Keep both sides balanced.
- Check by substitution.
Very beginner explanation: An equation stays balanced when equivalent operations are applied correctly.
Answer: x = 6
Worked Example 7
Problem: Solve 3x - 4 = 11.
- Simplify each side if needed.
- Use inverse operations to collect variable terms and constants.
- Keep both sides balanced.
- Check by substitution.
Very beginner explanation: An equation stays balanced when equivalent operations are applied correctly.
Answer: x = 5
Worked Example 8
Problem: Solve 5x + 7 = 2x + 22.
- Simplify each side if needed.
- Use inverse operations to collect variable terms and constants.
- Keep both sides balanced.
- Check by substitution.
Very beginner explanation: An equation stays balanced when equivalent operations are applied correctly.
Answer: x = 5
Worked Example 9
Problem: Solve 4(x + 2) = 24.
- Simplify each side if needed.
- Use inverse operations to collect variable terms and constants.
- Keep both sides balanced.
- Check by substitution.
Very beginner explanation: An equation stays balanced when equivalent operations are applied correctly.
Answer: x = 4
Worked Example 10
Problem: Solve 7x - 3 = 4x + 12.
- Simplify each side if needed.
- Use inverse operations to collect variable terms and constants.
- Keep both sides balanced.
- Check by substitution.
Very beginner explanation: An equation stays balanced when equivalent operations are applied correctly.
Answer: x = 5
Practice Exercise
Create one new question about Equations with negative numbers. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
23.11 Equations with decimals
A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Equations with decimals .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Identify the tenths digit in 3.47.
- The tenths digit is the first digit to the right of the decimal point.
Very beginner explanation: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Equations with decimals .
Answer: 4
Worked Example 2
Problem: Identify the tenths digit in 8.205.
- The tenths digit is the first digit to the right of the decimal point.
Very beginner explanation: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Equations with decimals .
Answer: 2
Worked Example 3
Problem: Identify the tenths digit in 0.96.
- The tenths digit is the first digit to the right of the decimal point.
Very beginner explanation: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Equations with decimals .
Answer: 9
Worked Example 4
Problem: Identify the tenths digit in 12.375.
- The tenths digit is the first digit to the right of the decimal point.
Very beginner explanation: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Equations with decimals .
Answer: 3
Worked Example 5
Problem: Identify the tenths digit in 5.004.
- The tenths digit is the first digit to the right of the decimal point.
Very beginner explanation: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Equations with decimals .
Answer: 0
Worked Example 6
Problem: Round 3.75 to the nearest tenth.
- Find the tenths digit.
- Look at the hundredths digit.
- Round up if the hundredths digit is 5 or more.
Very beginner explanation: Rounding uses the next digit to decide whether the target digit stays or increases.
Answer: 3.8
Worked Example 7
Problem: Round 8.4 to the nearest tenth.
- Find the tenths digit.
- Look at the hundredths digit.
- Round up if the hundredths digit is 5 or more.
Very beginner explanation: Rounding uses the next digit to decide whether the target digit stays or increases.
Answer: 8.4
Worked Example 8
Problem: Round 12.05 to the nearest tenth.
- Find the tenths digit.
- Look at the hundredths digit.
- Round up if the hundredths digit is 5 or more.
Very beginner explanation: Rounding uses the next digit to decide whether the target digit stays or increases.
Answer: 12.1
Worked Example 9
Problem: Round 0.96 to the nearest tenth.
- Find the tenths digit.
- Look at the hundredths digit.
- Round up if the hundredths digit is 5 or more.
Very beginner explanation: Rounding uses the next digit to decide whether the target digit stays or increases.
Answer: 1
Worked Example 10
Problem: Round 5.125 to the nearest tenth.
- Find the tenths digit.
- Look at the hundredths digit.
- Round up if the hundredths digit is 5 or more.
Very beginner explanation: Rounding uses the next digit to decide whether the target digit stays or increases.
Answer: 5.1
Practice Exercise
Create one new question about Equations with decimals. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
23.12 Checking solutions
Checking solutions is an important Grade 7 idea in One-Step and Two-Step Equations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Checking solutions: Identify a correct example.
- State the definition and show why the example fits.
- Show all important reasoning.
Very beginner explanation: Checking solutions is an important Grade 7 idea in One-Step and Two-Step Equations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 2
Problem: Checking solutions: Identify a non-example.
- Explain which requirement is missing.
- Show all important reasoning.
Very beginner explanation: Checking solutions is an important Grade 7 idea in One-Step and Two-Step Equations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 3
Problem: Checking solutions: Compare two cases.
- State one similarity and one difference.
- Show all important reasoning.
Very beginner explanation: Checking solutions is an important Grade 7 idea in One-Step and Two-Step Equations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 4
Problem: Checking solutions: Apply the idea in a real situation.
- Translate the situation into mathematical language.
- Show all important reasoning.
Very beginner explanation: Checking solutions is an important Grade 7 idea in One-Step and Two-Step Equations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 5
Problem: Checking solutions: Create and check your own example.
- Use the definition, then verify each condition.
- Show all important reasoning.
Very beginner explanation: Checking solutions is an important Grade 7 idea in One-Step and Two-Step Equations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 6
Problem: Explain Checking solutions in one simple sentence.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Checking solutions becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: State the meaning, then give one small example.
Worked Example 7
Problem: Give one example that does not satisfy Checking solutions and explain why.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Checking solutions becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Identify the rule or condition that fails.
Worked Example 8
Problem: Show Checking solutions using a table, diagram, number line, graph, or equation.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Checking solutions becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Choose the representation that makes the relationship easiest to see.
Worked Example 9
Problem: After solving a Checking solutions problem, how can you check the answer?
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Checking solutions becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Use estimation, an inverse operation, substitution, or a second representation.
Worked Example 10
Problem: Give one real-life situation where Checking solutions could be useful.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Checking solutions becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Connect the idea to money, measurement, data, design, or technology.
Practice Exercise
Create one new question about Checking solutions. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
23.13 Word problems
Word problems is an important Grade 7 idea in One-Step and Two-Step Equations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Word problems: Identify a correct example.
- State the definition and show why the example fits.
- Show all important reasoning.
Very beginner explanation: Word problems is an important Grade 7 idea in One-Step and Two-Step Equations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 2
Problem: Word problems: Identify a non-example.
- Explain which requirement is missing.
- Show all important reasoning.
Very beginner explanation: Word problems is an important Grade 7 idea in One-Step and Two-Step Equations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 3
Problem: Word problems: Compare two cases.
- State one similarity and one difference.
- Show all important reasoning.
Very beginner explanation: Word problems is an important Grade 7 idea in One-Step and Two-Step Equations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 4
Problem: Word problems: Apply the idea in a real situation.
- Translate the situation into mathematical language.
- Show all important reasoning.
Very beginner explanation: Word problems is an important Grade 7 idea in One-Step and Two-Step Equations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 5
Problem: Word problems: Create and check your own example.
- Use the definition, then verify each condition.
- Show all important reasoning.
Very beginner explanation: Word problems is an important Grade 7 idea in One-Step and Two-Step Equations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 6
Problem: Explain Word problems in one simple sentence.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Word problems becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: State the meaning, then give one small example.
Worked Example 7
Problem: Give one example that does not satisfy Word problems and explain why.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Word problems becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Identify the rule or condition that fails.
Worked Example 8
Problem: Show Word problems using a table, diagram, number line, graph, or equation.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Word problems becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Choose the representation that makes the relationship easiest to see.
Worked Example 9
Problem: After solving a Word problems problem, how can you check the answer?
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Word problems becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Use estimation, an inverse operation, substitution, or a second representation.
Worked Example 10
Problem: Give one real-life situation where Word problems could be useful.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Word problems becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Connect the idea to money, measurement, data, design, or technology.
Practice Exercise
Create one new question about Word problems. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
Chapter Notes, Practice, and Common Mistakes
Chapter Notes
- Read the complete question before choosing an operation, formula, graph, or model.
- Write technical words together with their meaning until you are comfortable using them.
- Show all important steps so another student can follow your reasoning.
- Keep units, labels, signs, axes, variables, and mathematical symbols clear.
- Estimate before or after calculating when an estimate can help check reasonableness.
- For real-life problems, explain what the final number means in the situation.
Extra Practice
- Create and solve a new question about Meaning of equation . Show your reasoning and check your answer.
- Create and solve a new question about Equality . Show your reasoning and check your answer.
- Create and solve a new question about Inverse operations . Show your reasoning and check your answer.
- Create and solve a new question about Addition equations . Show your reasoning and check your answer.
- Create and solve a new question about Subtraction equations . Show your reasoning and check your answer.
- Create and solve a new question about Multiplication equations . Show your reasoning and check your answer.
- Create and solve a new question about Division equations . Show your reasoning and check your answer.
- Create and solve a new question about Balancing equations . Show your reasoning and check your answer.
- Create and solve a new question about Two-step equations . Show your reasoning and check your answer.
- Create and solve a new question about Equations with negative numbers . Show your reasoning and check your answer.
- Create and solve a new question about Equations with decimals . Show your reasoning and check your answer.
- Create and solve a new question about Checking solutions . Show your reasoning and check your answer.
Common Mistakes
- Combining unlike terms.
- Changing only one side of an equation.
- Forgetting to distribute to every term.
- Using a pattern rule that works only for the first few terms.
- Writing code without tracing variable values.
- Using a mathematical model without stating assumptions.
30 Review Questions and Answers
Q1. What is important to remember about Meaning of equation?
Answer: An equation says that two expressions are equal. This topic focuses on Meaning of equation.
Q2. What is important to remember about Equality?
Answer: Equality is an important Grade 7 idea in One-Step and Two-Step Equations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q3. What is important to remember about Inverse operations?
Answer: A ratio compares two quantities in a fixed order. This topic focuses on Inverse operations.
Q4. What is important to remember about Addition equations?
Answer: An equation says that two expressions are equal. This topic focuses on Addition equations.
Q5. What is important to remember about Subtraction equations?
Answer: An equation says that two expressions are equal. This topic focuses on Subtraction equations.
Q6. What is important to remember about Multiplication equations?
Answer: A tip is an extra amount, often calculated as a percent of a bill. This topic focuses on Multiplication equations.
Q7. What is important to remember about Division equations?
Answer: An equation says that two expressions are equal. This topic focuses on Division equations.
Q8. What is important to remember about Balancing equations?
Answer: An equation says that two expressions are equal. This topic focuses on Balancing equations.
Q9. What is important to remember about Two-step equations?
Answer: An equation says that two expressions are equal. This topic focuses on Two-step equations.
Q10. What is important to remember about Equations with negative numbers?
Answer: An equation says that two expressions are equal. This topic focuses on Equations with negative numbers.
Q11. What is important to remember about Equations with decimals?
Answer: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Equations with decimals.
Q12. What is important to remember about Checking solutions?
Answer: Checking solutions is an important Grade 7 idea in One-Step and Two-Step Equations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q13. What is important to remember about Word problems?
Answer: Word problems is an important Grade 7 idea in One-Step and Two-Step Equations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q14. Why should you show your steps?
Answer: Showing steps makes reasoning easier to verify and helps locate mistakes.
Q15. Why is estimation useful?
Answer: Estimation helps you judge whether a final answer is reasonable before accepting it.
Q16. Why do units matter?
Answer: Units tell what a value measures and prevent incompatible quantities from being mixed.
Q17. When should you round?
Answer: Usually round near the end of a calculation unless the question specifically asks for earlier rounding.
Q18. How can you check an answer?
Answer: Use an inverse operation, substitution, estimation, a graph, or a second method.
Q19. What should you identify first in a word problem?
Answer: Identify what is known, what is unknown, and the relationship connecting them.
Q20. What makes a final answer complete?
Answer: Give the value, correct units when needed, and a brief interpretation in context.
Q21. What should you do if an answer seems unreasonable?
Answer: Re-read the question, check copied values, signs, units, formulas, and calculations.
Q22. Why are diagrams useful?
Answer: A labelled diagram can reveal relationships between lengths, angles, areas, and other quantities.
Q23. Why are tables useful?
Answer: Tables organize values and help reveal patterns, relationships, rates, and missing information.
Q24. Why should you explain your reasoning?
Answer: Reasoning shows why a method works, not just what answer you obtained.
Q25. How do mistakes help learning?
Answer: Analyzing a mistake identifies the misunderstood rule or step and helps prevent the same error later.
Q26. How should you study this chapter?
Answer: Review definitions, redo worked examples without looking, practise mixed questions, and explain solutions in your own words.
Q27. When is a calculator useful?
Answer: A calculator is useful for lengthy arithmetic after you understand the mathematical setup and can estimate the expected size of the answer.
Q28. Why compare more than one strategy?
Answer: Different strategies can make a problem easier and provide a way to verify the result.
Q29. What is a mathematical model?
Answer: It is a simplified mathematical representation of a real situation used to analyze, explain, or predict.
Q30. Why should assumptions be stated?
Answer: Assumptions show what conditions the solution depends on and help readers judge whether the model is reasonable.