Remove the fractions by multiplying every term by the lowest common denominator.
The lowest common denominator is the LCM of 4, 3 and 6 = 12.

$\begin{array}{rcl} 12 (\frac{3 x - 2}{4}) - 12 (\frac{2 x + 5}{3}) & = & 12 (\frac{1 - x}{6}) \end{array}$

[1]

Simplify by cancelling the common terms in each fraction.
The fractions should disappear.

$\begin{array}{rcl} 12 (\frac{3 x - 2}{4}) - 12 (\frac{2 x + 5}{3}) & = & 12 (\frac{1 - x}{6}) \\ 3 (3 x - 2) - 4 (2 x + 5) & = & 2 (1 - x) \end{array}$

[1]

Expand all three sets of brackets.
Remember to expand both parts of the bracket and be careful with the negative sign.

$\begin{array}{rcl} 9 x - 6 - 8 x - 20 & = & 2 - 2 x \end{array}$

Simplify the left hand side.

$\begin{array}{rcl} 9 x - 8 x - 6 - 20 & = & 2 - 2 x \\ x - 26 & = & 2 - 2 x \end{array}$

Bring the x terms to one side by adding 2x to both sides and the number terms to the other by adding 26 to both sides.

$\begin{array}{rcl} x - 26 & = & 2 - 2 x \\ + 2 x & = & + 2 x \\ 3 x - 26 & = & 2 \\ + 26 & = & + 26 \\ 3 x & = & 28 \end{array}$

[1]

Divide both sides by 3.

$x = \frac{28}{3}$

$x = 9 \frac{1}{3}$ [1]

The improper fraction is also accepted.

Linear Equations (AQA GCSE Maths)

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