How to Solve Equations With Variables on Both Sides

Equations with variables on both sides look more complicated, but they still follow the balance rule.

Quick idea

Collect variable terms on one side and number terms on the other side.

Steps

1. Simplify each side if needed.
2. Move the smaller variable term to the other side.
3. Move constants to the opposite side.
4. Divide to isolate the variable and check.

Worked example

Solve 3x plus 2 equals x plus 10.

Full solution

Step-by-step walkthrough

Step 1

Subtract x from both sides to get 2x plus 2 equals 10.

Step 2

Subtract 2 from both sides.

Step 3

Divide by 2 to get x equals 4.

Common mistake

Moving a term across the equal sign means doing the inverse operation to both sides, not just changing signs randomly.

Practice problems

1. Solve 4x + 1 = 2x + 9.
2. Solve 5y - 3 = 2y + 12.
3. Solve 7a + 4 = 3a + 20.

Answers

1. x = 4
2. y = 5
3. a = 4

Ask Pennpaper to explain it live

If the steps make sense but you still feel stuck, start a Pennpaper lesson and ask the tutor to draw the problem on the whiteboard. Seeing the symbols move step by step is often what makes the concept click.

Related guides

• How to Solve Two-Step Equations
• How to Turn Word Problems Into Equations
• How to Solve Systems of Equations by Substitution