How to Solve Linear Equations (KS3): A Step-by-Step Guide

Solving equations is one of the first big ideas in KS3 algebra — and once it clicks, a huge amount of later maths falls into place. The golden rule is simple:

Whatever you do to one side of the equation, you must do to the other.

One-step equations

Suppose we want to solve:

The $x$ has $7$ added to it, so we subtract 7 from both sides to undo that:

Two-step equations

Now try:

We undo in reverse order. First subtract $4$ from both sides, then divide by $3$:

Common mistakes

• Only changing one side of the equation.
• Forgetting the order: undo addition/subtraction before multiplication/division.
• Dropping a negative sign when subtracting.

The best way to lock this in is practice — try the questions in the KS3 papers, or power up your octopus solving equations in the game.