How to Solve for X: A Step-by-Step Guide

When you see an equation like 2x + 5 = 13, your job is to find what x equals. "Solving for x" means getting x alone on one side of the equals sign. Here's how.

The main idea

An equation is like a balance scale: whatever you do to one side, you must do to the other to keep it equal. To solve for x, we use inverse operations — operations that undo each other. Addition undoes subtraction; multiplication undoes division.

One-step equations

When only one operation is applied to x, undo it with the inverse.

Example 1: x + 7 = 12

7 is added to x. Subtract 7 from both sides:

Answer: x = 5

Example 2: 3x = 15

x is multiplied by 3. Divide both sides by 3:

Answer: x = 5

Two-step equations

When two operations are applied, undo them in reverse order (undo addition/subtraction first, then multiplication/division).

Example: 2x + 5 = 13

Step 1: Subtract 5 from both sides to remove the +5.

Step 2: Divide both sides by 2 to get x alone.

Answer: x = 4

Check: 2(4) + 5 = 8 + 5 = 13 ✓

Quick reference

• x + a = b → subtract a from both sides
• x − a = b → add a to both sides
• ax = b → divide both sides by a
• x ÷ a = b → multiply both sides by a

Common mistakes

Forgetting to do both sides: Whatever you do to one side of the equation, you must do to the other. If you subtract 5 from the left, subtract 5 from the right too.

Sign errors: Moving a negative across the equals sign turns it positive, and vice versa. Double-check your signs at each step.

Dividing before subtracting: In two-step equations like 3x + 7 = 22, undo addition/subtraction first, then multiplication/division.

More examples

Example: 4x − 9 = 15

Example: x/3 + 2 = 8

Example: −2x + 10 = 4

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