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Summary Grade 8 Mathematics Made Easy – Part 2: Linear Equations & Inequalities

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Second Year / 8th Grade
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Mathematics
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Original, student-friendly Grade 8 Mathematics study reviewer covering linear equations and inequalities. This reviewer includes one-step and two-step equations, equations with variables on both sides, the distributive property, equations with fractions, linear inequalities, graphing inequalities on a number line, word problems, worked examples, a quick review section, and a 20-item practice quiz with answer key. Designed as a clear and easy-to-use study guide for Grade 8 students.

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GRADE 8
MATHEMATICS MADE EASY

Part 2: Linear Equations & Inequalities



Student-Friendly Study Reviewer

, Table of Contents
• 1. Understanding Linear Equations

• 2. One-Step Equations

• 3. Two-Step Equations

• 4. Variables on Both Sides

• 5. Distributive Property

• 6. Equations with Fractions

• 7. Linear Inequalities

• 8. Graphing Inequalities

• 9. Word Problems

• 10. Worked Examples

• 11. Quick Review

• 12. 20-Item Practice Quiz

• 13. Answer Key


1. Understanding Linear Equations
A linear equation is an equation in which the variable has a degree of 1. A solution is a value that makes the
equation true.

Example: x + 5 = 12. The solution is x = 7 because 7 + 5 = 12.

The goal when solving an equation is to isolate the variable on one side while keeping the equation balanced.


2. One-Step Equations
Use the inverse operation to isolate the variable.

Addition: x + 8 = 15 → subtract 8 from both sides → x = 7.

Subtraction: x − 6 = 10 → add 6 to both sides → x = 16.

Multiplication: 4x = 28 → divide both sides by 4 → x = 7.

Division: x/5 = 9 → multiply both sides by 5 → x = 45.


3. Two-Step Equations
For a two-step equation, undo addition or subtraction first, then undo multiplication or division.

Example: 3x + 4 = 19. Subtract 4: 3x = 15. Divide by 3: x = 5.


4. Variables on Both Sides

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