Solving Linear Equations: Complete Guide
Solving equations is the backbone of GCSE algebra. The golden rule: whatever you do to one side, do to the other to keep the equation balanced.
The balance method
An equation is like a set of balanced scales. To solve it, undo the operations using inverse operations (the opposite), keeping both sides equal.
- The inverse of + is −
- The inverse of × is ÷
- The inverse of squaring is square-rooting
Worked example: two-step equation
Solve 2x + 3 = 11
Unknowns on both sides
Solve 5x − 2 = 3x + 8
- Forgetting to do the operation to both sides
- Sign errors when moving terms across the equals sign
- Not expanding brackets first, e.g. 3(x − 2) = 9 becomes 3x − 6 = 9
Frequently asked questions
What is the balance method?
It means doing the same operation to both sides of an equation so it stays balanced, using inverse operations to isolate the unknown.
How do I solve equations with brackets?
Expand the brackets first, then collect like terms and use inverse operations. For example 3(x - 2) = 9 becomes 3x - 6 = 9, so 3x = 15 and x = 5.
How do I solve equations with x on both sides?
Move all the x terms to one side and the numbers to the other by adding or subtracting the same thing from both sides, then divide.
Ready to practise?
Try interactive questions with instant feedback and worked solutions.
Start practising →