Algebra › Equations

Equations

An equation is a balance. The equals sign means the two sides weigh the same — and you have to keep them that way.

Balance the equation

Whatever you do to one side, do to the other.

x + 3 = 12

x + 3

Subtract 3 from both sides, then solve.

The golden rule

Whatever you do to one side of the equation, do to the other. Add 5 to one side, add 5 to the other. Divide by 2 on the left, divide by 2 on the right. The two sides start equal — your job is to keep them equal.

The goal

Get the unknown letter (usually x) all alone on one side. The other side will then tell you what x is.

Inverse operations

To get rid of + 3, subtract 3. To undo × 4, divide by 4. Each operation has its inverse — that's the move that cancels it.

Walked-through example

Solve 2x + 4 = 14:

Subtract 4 from both sides: 2x = 10.
Divide both sides by 2: x = 5.
Check by substituting back: 2(5) + 4 = 14. ✓

Quick check

Solve 2x − 6 = 4. What is x?