How to Solve One-Step Equations

An equation is like a balance scale: both sides must stay equal. Solving means finding the value that makes the sentence true.

Quick idea

Use the inverse operation to undo what is happening to the variable.

Steps

1. Find what operation is attached to the variable.
2. Use the opposite operation on both sides.
3. Simplify to isolate the variable.
4. Substitute the answer back into the original equation to check.

Worked example

Solve x plus 7 equals 12.

Full solution

Step-by-step walkthrough

Step 1

The variable has 7 added to it.

Step 2

Undo addition by subtracting 7 from both sides.

Step 3

The solution is x equals 5.

Common mistake

Whatever you do to one side, you must do to the other side. That is what keeps the equation balanced.

Practice problems

1. Solve x + 4 = 9.
2. Solve y - 6 = 10.
3. Solve 3a = 18.

Answers

1. x = 5
2. y = 16
3. a = 6

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 Equations With Variables on Both Sides