Year 9 Interactive Maths - Second Edition

Linear Inequalities

A number can be subtracted from each side of an inequality as illustrated below.

If you put 10 kilograms in one of a pair of scales and add 6 kilograms to the other, the scales
will show that 10 kg is heavier than 6 kg.  

Take 2 kg away from each side

In general:

Subtracting the same number from both sides of an inequality does not change the inequality's sign.

Example 21

Solution:

Note:

(i)  The solution set consists of all numbers greater than 4, and is shown on the number line as follows:

      The ring at 4 in this diagram means that 4 is not an element of the solution set. 

Example 22

Solution:

Note:

(i)  The solution set consists of all numbers less than or equal to –2, as shown on the following number line.

      The solid dot at –2 in the diagram means that –2 is an element of the solution set.

Key Terms

linear inequality