IGCSE · Practice questions · Forming and solving linear equations

Same to both sides.

Six original Cambridge-style questions on forming and solving linear equations, including fractional equations and a problem in context.

Original questions All questions on this page are original work, written in the Cambridge IGCSE style. They are not from past papers. They test the same concepts and skills the syllabus rewards.

The method

Expand, collect, divide, check.

Fractions (Extended): multiply every term by the common denominator first.
Brackets: expand, watching the sign of the number outside.
Collect: unknowns on the side where they stay positive, numbers on the other.
Divide: by the number in front of the unknown.
Check: substitute into the original equation; answer what was asked.

Recall

[2 marks]

Solve (a) $7x - 3 = 25$ (b) $\dfrac{x}{5} + 6 = 2$.

(a) $7x = 28$, $x = 4$ ✓
(b) $\dfrac{x}{5} = -4$, $x = -20$ ✓

Calculation

[3 marks]

Solve $3(2x - 5) = 4x + 9$.

$6x - 15 = 4x + 9$ ✓
$2x = 24$ ✓
$x = 12$ ✓

Calculation

[3 marks]

Solve $8 - 3(x - 2) = 2(x + 4)$.

$8 - 3x + 6 = 2x + 8$ ✓
$14 - 3x = 2x + 8$, so $6 = 5x$ ✓
$x = 1.2$ ✓

Analysis

[4 marks]

A rectangle has width $w$ cm. Its length is 3 cm more than twice its width. The perimeter is 42 cm.

(a) Write an equation in $w$. (b) Solve it and find the area of the rectangle.

(a) $2(w + 2w + 3) = 42$ ✓
(b) $6w + 6 = 42$, $6w = 36$, $w = 6$ ✓
Length $= 2(6) + 3 = 15$ cm ✓
Area $= 6 \times 15 = 90$ cm² ✓

Calculation

[3 marks]

(Extended) Solve $\dfrac{5}{x + 1} = \dfrac{2}{x - 2}$.

$5(x - 2) = 2(x + 1)$ ✓
$5x - 10 = 2x + 2$, so $3x = 12$ ✓
$x = 4$ ✓

Analysis

[5 marks]

Phone plan A costs $12 per month plus $0.05 per minute of calls. Plan B costs $20 per month plus $0.03 per minute.

(a) For $m$ minutes of calls, write an equation for when the two plans cost the same.

(b) Solve your equation.

(a) $12 + 0.05m = 20 + 0.03m$ ✓
(b) $0.02m = 8$, so $m = 400$ minutes ✓
(c) A: $12 + 0.05 \times 500 = \$37$. B: $20 + 0.03 \times 500 = \$35$ ✓
Plan B is cheaper by $2. ✓

Mark this once you have attempted all six and checked your working. It records a Practiced badge on the topic and adds a one-time bonus. Revealing the solutions alone does not count.