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Solving linear equations

Solve linear equations using inverse operations. Covers one- and two-step equations, equations with variables on both sides, brackets, and fractions.

Worked examples

Two-step equation

Straightforward

Problem

Solve for xx.
2x+3=112x + 3 = 11

Equation with brackets and variable on both sides

Moderate

Problem

Solve for xx.
3(x+2)=2x+93(x + 2) = 2x + 9

Equation with fractions on both sides

Challenging

Problem

Solve for xx.
2x+13=x−12\dfrac{2x + 1}{3} = \dfrac{x - 1}{2}

Practise

Q1·Straightforward
Solve for xx.
3x+4=193x + 4 = 19
Q2·Straightforward
Solve for xx.
x2−1=5\dfrac{x}{2} - 1 = 5
Q3·Straightforward
Solve for xx.
2x−7=112x - 7 = 11
Q4·Straightforward
Solve for xx.
5+4x=295 + 4x = 29
Q5·Moderate
Solve for xx.
3(x+2)=2x+93(x + 2) = 2x + 9
Q6·Moderate
Solve for xx.
5x−3=2x+125x - 3 = 2x + 12
Q7·Moderate
Solve for xx.
2(3x−1)=4x+82(3x - 1) = 4x + 8
Q8·Moderate
Solve for xx.
4(x−3)=2(x+1)4(x - 3) = 2(x + 1)
Q9·Challenging
Solve for xx.
2x+13=x−12\dfrac{2x + 1}{3} = \dfrac{x - 1}{2}
Q10·Challenging
Solve for xx.
x4+x3=7\dfrac{x}{4} + \dfrac{x}{3} = 7
Q11·Challenging
Solve for xx.
x+32−x−14=3\dfrac{x + 3}{2} - \dfrac{x - 1}{4} = 3
Q12·Challenging
Solve for xx.
3(2x−1)−2(x+4)=53(2x - 1) - 2(x + 4) = 5