Year 9 Interactive Maths - Second Edition

Multiplying Each Side of an Inequality by a Positive Number

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

If we double the weight on both sides, then we have (2 × 10) kg = 20 kg outweighing (2 × 6) kg =12 kg.  That is:

Multiply each side by 2

In general:

Both sides of an inequality can be multiplied by the same positive number.

Example 24

Solution:

Note:

(i)  The solution set consists of all numbers less than or equal to 6, and is shown on the number line as follows:

      The solid dot at 6 in this diagram means that 6 is an element of the solution set.