Year 9 Interactive Maths - Second Edition

Adding a Number to Each Side of an Inequality

A number can be added to 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.  That is, 10 > 6.

Adding 2 kg to each scale will result in 12 kg on one side and 8 kg on the other.  Then the scales will show that 12 kg is heavier than 8 kg.  That is:

Add 2 kg to each side

In general:

Subtracting or adding a number to both sides of an inequality does not change the inequality's sign.

Example 23

Solution:

Note:

(i)  The solution set consists of all numbers greater than or equal to 5, and is shown on the number line as follows:

      The solid dot at 5 in this diagram means that 5 is an element of the solution set.