The Golden Rule of Algebra

ALGEBRA

Algebra is not about "finding x". It is about balance. Think of an equation like a weighing scale. If you keep both sides balanced, you can solve anything!

Key Words You Need to Know

Variable x, y, a

The unknown letter.

Coefficient 3x

The number multiplying the variable (Here, it is 3).

Constant + 5

A number on its own.

⚖️ The Golden Rule of Algebra:
Whatever you do to one side of the equation (add, subtract, multiply, divide), you MUST do to the other side.

How to Solve Equations

Example 1: Addition

Solve for x: x + 4 = 10

• Goal: Get 'x' by itself.
• Problem: The '+ 4' is in the way.
• Action: Do the opposite. Subtract 4 from BOTH sides.

x + 4 - 4 = 10 - 4

Answer: x = 6

Example 2: Multiplication

Solve for y: 3y = 15

• Goal: Get 'y' by itself.
• Problem: It is multiplied by 3.
• Action: Do the opposite. Divide BOTH sides by 3.

3y ÷ 3 = 15 ÷ 3

Answer: y = 5

Example 3: Two-Step Equation

Solve for a: 2a - 5 = 11

Step 1: Get rid of the -5 first (Add 5).

2a - 5 + 5 = 11 + 5
2a = 16

Step 2: Get rid of the 2 (Divide by 2).

2a ÷ 2 = 16 ÷ 2

Answer: a = 8

---

⚡ Rapid Fire Algebra Quiz

Can you balance the scales? Try these 4 questions.

1. Solve for x: x + 7 = 15

A) x = 22 B) x = 8

Incorrect. Subtract 7 from 15. (15 - 7 = 8).

Correct! 15 - 7 = 8.

2. Solve for y: 5y = 20

A) y = 4 B) y = 100

Incorrect. Opposite of multiply is divide. 20 ÷ 5 = 4.

Correct! 20 ÷ 5 = 4.

3. Solve for m: m/2 = 6

A) m = 3 B) m = 12

Incorrect. m is divided by 2. To fix it, MULTIPLY by 2. 6 × 2 = 12.

Correct! Opposite of divide is multiply. 6 × 2 = 12.

4. Solve: 3x + 2 = 17

A) x = 5 B) x = 6

Incorrect. First subtract 2 (gives 15). Then divide by 3 (15 ÷ 3 = 5).

Correct! 17 - 2 = 15. Then 15 ÷ 3 = 5.