Solving Linear Inequalities (Edexcel GCSE Maths: Foundation): Revision Note

• Do not change the inequality sign to an equals when solving linear inequalities.

  • In an exam you will lose marks for doing this. 

• Remember to reverse the direction of the inequality sign when multiplying or dividing by a negative number!

Solve the inequality $2x-5\le 21$.

Answer:

Add 5 to both sides

$2x\le 26$

Now divide both sides by 2

$x\le 13$

$\mathit{x}\mathbf{\le }\mathbf{13}$ 

Solve the inequality $5-2x\le 21$.

Answer:

Subtract 5 from both sides, keeping the inequality sign the same

$-2x\le 16$

Now divide both sides by -2.
However because you are dividing by a negative number, you must flip the inequality sign

$\mathit{x}\mathbf{\ge }\mathbf{-}\mathbf{8}$ or $\mathbf{-}\mathbf{8}\mathbf{\le }\mathit{x}$

Solve the inequality $-7\le 3x-1<2$, illustrating your answer on a number line.

Answer:

This is a double inequality, so any operation carried out to one side must be done to all three parts
Use the expression in the middle to choose the inverse operations needed to isolate x

Add 1 to all three parts
Remember not to change the inequality signs

$-6\le 3x<3$

Divide all three parts by 3
3 is positive so there is no need to flip the signs

$\mathbf{-}\mathbf{2}\mathbf{\le }\mathit{x}\mathbf{<}\mathbf{1}$

Illustrate the final answer on a number line, using an open circle at 1 and a closed circle at -2.