Get rid of the fractions by multiplying both sides by the denominators. Use brackets around expressions when multiplying.

$\begin{array}{rcl} \frac{2 x + 5}{3 - x} \times (3 - x) \times 15 & = & \frac{14}{15} \times (3 - x) \times 15 \\ (2 x + 5) \times 15 & = & 14 \times (3 - x) \\ 15 (2 x + 5) & = & 14 (3 - x) \end{array}$

[1]

Expand both brackets.

$30 x + 75 = 42 - 14 x$

[1]

Get all the x terms on one side.
Add 14x to both sides.

$\begin{array}{rcl} 30 x + 75 + 14 x & = & 42 \\ 44 x + 75 & = & 42 \end{array}$

Get the x term alone on one side.
Subtract 75 from both sides.

$44 x = 42 - 75 44 x = - 33$

Divide both sides by 44.

$x = - \frac{33}{44}$

Simplify the fraction.

$x = - \frac{3}{4}$ [1]
It is also acceptable to write as a decimal: $x = - 0.75$

Linear Equations & Inequalities (Cambridge O Level Maths)

Exam Questions