Year 9 Interactive Maths - Second Edition

Multiplying Each Side of an Inequality by a Negative Number

Consider the inequality

15 > 10

If we multiply both sides by –2, we get –2 × 15 = –30 on the left-hand side and –2 × 10 = –20 on the right-hand side.  If we think of temperature we can see that –20 degrees is higher than –30 degrees.  So, to get a true statement we have to reverse the 'greater than' sign.

Let us consider another example.

Consider the inequality

5 < 8

If we multiply both sides by –3, we get –3 × 5 = –15 on the left-hand side and –3 × 8 = –24 on the right-hand side.  So, we must reverse the 'less than' sign to get a true statement.

In general:

If both sides of an inequality are multiplied by the same negative number, then:

Example 26

Solution:

Example 27

Solution: