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Solving Linear Equations GCSE Maths

Solving linear equations is a core GCSE Maths skill. The aim is to find the value of the unknown, usually x, that makes the equation true.

The main rule is simple: whatever you do to one side, you must do to the other side as well.

What Is a Linear Equation?

A linear equation is an equation where the variable has power 1.

Example:

2x + 5 = 17

We want to work out the value of x.

Example 1: Two-Step Equation

2x + 5 = 17

Step 1: Subtract 5 from both sides

2x = 12

Step 2: Divide both sides by 2

x = 6

Example 2: Variable on Both Sides

3x + 4 = x + 10

Step 1: Move x terms to one side

Subtract x from both sides:

2x + 4 = 10

Step 2: Move numbers to the other side

Subtract 4 from both sides:

2x = 6

Step 3: Divide by 2

x = 3

Example 3: Brackets in an Equation

3(x + 2) = 18

Step 1: Expand the bracket

3x + 6 = 18

Step 2: Subtract 6 from both sides

3x = 12

Step 3: Divide by 3

x = 4

How to Check Your Answer

Substitute your answer back into the original equation.

For example, if x = 6 in 2x + 5 = 17:

2(6) + 5 = 12 + 5 = 17

So the answer is correct.

Common Mistakes

  • doing different operations to each side
  • sign mistakes when moving terms
  • forgetting to expand brackets first
  • losing track of negative numbers
  • not checking the final answer

Quick Practice Questions

  1. x + 7 = 19
  2. 3x = 24
  3. 2x + 9 = 21
  4. 5x - 6 = 14
  5. 4x + 3 = 2x + 11

Answers

  1. x = 12
  2. x = 8
  3. x = 6
  4. x = 4
  5. x = 4

Final Tip

Try to keep the variable on one side and the numbers on the other. Work one step at a time and check your answer at the end.