GCSE maths · Algebra
Solving linear equations
Revision notes for Foundation and Higher. Three ideas, each with a worked example, the reason for every line, and the trap to avoid.
Every worked example was checked by the code that marks Mathable’s tests.
1Balance both sides
Whatever you do to one side of the equation, do exactly the same to the other side.
Think of it like
An equation is a set of scales: take or add the same weight from both pans to keep it level.
Worked example
Solve 5x + 4 = 2x + 19.
- take 2x both sides
- take 4 both sides
- Answerdivide both sides by 3
TrapIf you subtract 2x from the left but not the right, the sides stop being equal.
Explain it back
Why does doing the same thing to both sides keep the equation true?
Say it out loud in two or three sentences. Where you get stuck is what to revise.
2Collect terms onto one side
Move all the x terms to one side and all the numbers to the other, then simplify.
Think of it like
Sort a mixed pile of coins and notes into two separate piles before counting each one.
Worked example
Solve 6x - 5 = 2x + 11.
- take 2x from both sides
- add 5 both sides
- Answerdivide both sides by 4
TrapIf you move a term without changing its sign, both sides stop matching.
Explain it back
Why do you change a term's sign when moving it across?
3Check by substituting
Put your answer back into the original equation to check both sides match.
Think of it like
Like trying a key in a lock: if it turns smoothly, it was the right key.
Worked example
Solve 5x + 2 = 3x + 14, then check your answer.
- subtract 3x both sides
- subtract 2 both sides
- divide both sides by 2
- check both sides equal
- Answer
TrapIf you substitute into only one side, you cannot actually tell if it checks out.
Explain it back
Why does substituting your answer into both sides prove it's right?
Practise with Mathable
Practise solving equations with a tutor that checks every line
- ›Ten questions on solving equations, marked for you.
- ›It points at the first mistake in your working.
- ›One hint at a time, so you work out the fix yourself.
- ›Explain an idea back, and it tells you the one gap.
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