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Equations with fractions

Solve equations involving fractions by multiplying both sides to clear the denominator.

Worked examples

Solving $\frac{x}{a} = b$

Straightforward

Problem

Solve for xx:
x7=5\frac{x}{7} = 5

Solving $\frac{x + a}{b} = c$

Moderate

Problem

Solve for xx:
x+53=8\frac{x + 5}{3} = 8

Solving equations with fractions on both sides

Challenging

Problem

Solve for xx:
x4=x+97\frac{x}{4} = \frac{x + 9}{7}

Practise

Q1·Straightforward
Solve for xx:
x4=7\frac{x}{4} = 7
Q2·Straightforward
Solve for xx:
x3=9\frac{x}{3} = 9
Q3·Straightforward
Solve for xx:
x5=6\frac{x}{5} = 6
Q4·Straightforward
Solve for xx:
x6=4\frac{x}{6} = 4
Q5·Moderate
Solve for xx:
x+34=5\frac{x + 3}{4} = 5
Q6·Moderate
Solve for xx:
x−23=6\frac{x - 2}{3} = 6
Q7·Moderate
Solve for xx:
2x+15=3\frac{2x + 1}{5} = 3
Q8·Moderate
Solve for xx:
3x−42=7\frac{3x - 4}{2} = 7
Q9·Challenging
Solve for xx:
x2=x+65\frac{x}{2} = \frac{x + 6}{5}
Q10·Challenging
Solve for xx:
x3=x+87\frac{x}{3} = \frac{x + 8}{7}
Q11·Challenging
Solve for xx:
x+13=x−12\frac{x + 1}{3} = \frac{x - 1}{2}
Q12·Challenging
Solve for xx:
2x+13=x+42\frac{2x + 1}{3} = \frac{x + 4}{2}