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)

Exam Questions

1. Number

Number Toolkit

Prime Factors, HCF & LCM

Powers, Roots & Standard Form

Fractions

Percentages

Simple & Compound Interest, Growth & Decay

Fractions, Decimals & Percentages

Rounding, Estimation & Bounds

Surds

Using a Calculator

2. Algebra

Algebra Toolkit

Algebraic Roots & Indices

Expanding Brackets

Factorising

Completing the Square

Algebraic Fractions

Rearranging Formulae

Algebraic Proof

Linear Equations

Solving Quadratic Equations

Simultaneous Equations

Iteration

Forming & Solving Equations

Functions

Coordinate Geometry

Linear Graphs y = mx + c

Graphs of Functions

Equation of a Circle

Estimating Gradients & Areas under Graphs

Real-Life Graphs

Solving Inequalities

Graphing Inequalities

Transformations of Graphs

Sequences

3. Ratio, Proportion & Rates of Change

Ratio Toolkit

Ratio Problem Solving

Direct & Inverse Proportion

Standard & Compound Units

Exchange Rates & Best Buys

4. Geometry & Measures

Geometry Toolkit

Angles in Polygons & Parallel Lines

Bearings, Scale Drawing, Constructions & Loci

Circle Theorems

Area & Perimeter

Circles, Arcs & Sectors

Volume & Surface Area

Congruence, Similarity & Geometrical Proof

Area & Volume of Similar Shapes

Right-Angled Triangles - Pythagoras & Trigonometry

Sine, Cosine Rule & Area of Triangles

3D Pythagoras & Trigonometry

Vectors

Transformations

5. Probability

Probability Toolkit

Simple Probability Diagrams

Tree Diagrams

Combined & Conditional Probability

6. Statistics

Statistics Toolkit

Statistical Diagrams

Histograms

Cumulative Frequency & Box Plots

Scatter Graphs & Correlation