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Topic 1 of 5 Level 1 — Beginner ⏱️ ~20 minutes

Algebra — Simplification & Equations

Learn how to work with variables, simplify algebraic expressions, and solve linear equations — one of the most important foundations of Mathematics at WAEC level.

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Notes
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Examples
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Practice
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Study Notes

What is Algebra?

Algebra is a branch of mathematics where we use letters (called variables) to represent unknown numbers. Instead of saying "a number plus 5 equals 8," we write x + 5 = 8. Our job is to find what value of x makes this true.

Variables are usually letters like x, y, a, or n. The number in front of a variable is called the coefficient. In 3x, the coefficient is 3.

Like Terms — What Can You Combine?

Like terms are terms that have the exact same variable part. You can only add or subtract like terms.

Remember: Think of it like fruit. 3 apples + 5 apples = 8 apples. But 3 apples + 5 oranges cannot be simplified — they are different things, just like 3x and 5y.

Simplifying Expressions

To simplify an algebraic expression, collect all like terms together and combine them.

Simplify: 5x + 3y + 2x − y = (5x + 2x) + (3y − y) = 7x + 2y

Always work through the expression carefully, grouping the same variables together before combining.

Solving Linear Equations

A linear equation has a variable with no power higher than 1. To solve it, you need to get the variable alone on one side of the equals sign.

The golden rule: whatever you do to one side, you must do to the other side.

Solve: 2x + 6 = 14 Step 1: Subtract 6 from both sides → 2x = 8 Step 2: Divide both sides by 2 → x = 4
Key operations: Add, subtract, multiply, or divide both sides equally. The balance of the equation must always be maintained.

Equations with Variables on Both Sides

Sometimes the variable appears on both sides of the equation. Move all variable terms to one side and all number terms to the other.

Solve: 5x − 3 = 2x + 9 Step 1: Subtract 2x from both sides → 3x − 3 = 9 Step 2: Add 3 to both sides → 3x = 12 Step 3: Divide both sides by 3 → x = 4
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Worked Examples
Example 1
Simplify: 4a + 7b − 2a + 3b
Step 1
Group the like terms together — 'a' terms with 'a' terms, 'b' terms with 'b' terms. (4a − 2a) + (7b + 3b)
Step 2
Combine each group. 2a + 10b
✓ Answer:2a + 10b
Example 2
Solve for x: 3x + 10 = 25
Step 1
Subtract 10 from both sides to isolate the term with x. 3x + 10 − 10 = 25 − 10 → 3x = 15
Step 2
Divide both sides by 3. 3x ÷ 3 = 15 ÷ 3 → x = 5
Check
Substitute x = 5 back into the original equation to verify. 3(5) + 10 = 15 + 10 = 25 ✓
✓ Answer:x = 5
Example 3
Solve: 6x − 4 = 2x + 12
Step 1
Move all x terms to the left — subtract 2x from both sides. 6x − 2x − 4 = 12 → 4x − 4 = 12
Step 2
Add 4 to both sides. 4x = 16
Step 3
Divide both sides by 4. x = 4
✓ Answer:x = 4
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Practice Questions

Topic 1 Practice Quiz

5 questions on Algebra. Score 4 or more (80%) to complete this topic and move on.

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