Key ideas
Balancing
An equation is like a balance: both sides are equal.
Whatever you do to one side, do the same to the other.
Undo it
+ is undone by −, and − by +.
× is undone by ÷, and ÷ by ×.
Two steps: undo the + or − first, then the × or ÷.
Brackets
Expand the bracket first, then solve.
Check
Put your answer back into the equation. Both sides should match.
2x + 3 = 11
Typing answers: type x = 5 (or just 5).
One-step equations
Solve x + 7 = 15.(1 mark)
Take 7 from both sides.x + 7 − 7 = 15 − 7 − 7 both sidesx = 8✓1Check: 8 + 7 = 15 ✓
In plain EnglishThe + 7 is undone by taking away 7. Do it to both sides to keep the balance.
Solve 4x = 28.(1 mark)
Divide both sides by 4.x = 284 ÷ 4 both sidesx = 7✓1
In plain English4x means 4 × x. Undo × 4 by dividing by 4.
Two-step equations
Solve 2x + 3 = 11.(2 marks)
Take 3 from both sides.2x = 8 − 3 both sides✓1
In plain EnglishTake 3 cubes off both sides of the balance.
Divide both sides by 2.x = 82 ÷ 2 both sidesx = 4✓2Check: 2 × 4 + 3 = 11 ✓
In plain EnglishTwo bags balance 8 cubes, so one bag balances 4.
Equations with a bracket
Solve 3(x + 2) = 21.(3 marks)
Expand.3x + 6 = 21✓1
In plain EnglishMultiply both terms in the bracket by 3.
Take 6 from both sides.3x = 15 − 6✓2
In plain EnglishTake 6 from both sides to get the x terms on their own.
Divide by 3.x = 5✓3
In plain English3x means 3 × x, so divide both sides by 3.
Unknowns on both sides (extension)
Solve 5x + 2 = 3x + 10.(3 marks)
Take 3x from both sides.2x + 2 = 10 − 3x both sides✓1
In plain EnglishGet all the x terms on one side. Take away the smaller amount of x.
Take 2 from both sides.2x = 8 − 2✓2
In plain EnglishTake 2 from both sides to leave the x terms on their own.
Divide.x = 4✓3Check: 5 × 4 + 2 = 22, 3 × 4 + 10 = 22 ✓
In plain EnglishDivide both sides by 2. Check by putting x = 4 back into both sides: they should match.
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Your turn
Type answers like x = 5 (or just 5). Use a minus sign for negative answers. Stuck? Tap Need a hint?