Solving linear equations · Cambridge IGCSE Mathematics

In plain words

An equation is a balance: the two sides are equal. You can do anything to it as long as you do the same to both sides. The aim is to peel things away from the x until it stands alone.

Three things to know

Undo what has been done to x, in reverse order, doing the same to both sides.
If there are brackets, expand them first. If x is on both sides, collect the x terms on one side.
If there's a fraction, multiply both sides by the denominator to get rid of it.

Worked example

Solve 5x − 3 = 2x + 9.

Take 2x from both sides: 3x − 3 = 9.
Add 3 to both sides: 3x = 12.
Divide both sides by 3: x = 4.

Tips and tricks

Put your answer back into the original equation. 5(4) − 3 = 17 and 2(4) + 9 = 17, so it's right.
Write a new line for each step, with the equals signs lined up. It's easier to check and it shows your method.

5 questions, about 2 minutes.

It lands in your notebook with its questions as flashcards.

Solving linear equations: 5 questions and answers

These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.

Solve 2x + 5 = 17.
- x = 11
- x = 6 (the answer)
- x = 12
- x = 8.5
2x = 12.
Solve 3(x + 1) = 21.
- x = 7
- x = 6 (the answer)
- x = 20/3
- x = 8
x + 1 = 7.
Solve x/4 = 5.
- x = 1.25
- x = 9
- x = 20 (the answer)
- x = 1
Multiply both sides by 4.
Solve 6x − 4 = 2x + 8.
- x = 1
- x = 2
- x = 3 (the answer)
- x = 12
4x = 12.
Solve 5x = −15.
- x = 3
- x = −3 (the answer)
- x = −75
- x = −20
Divide both sides by 5.

5 questions

Tap an answer and you’ll see straight away whether it’s right, and why.

Worksheet

4 questions, 9 marks. Write your answers on paper, then check them.