Operations on Inequalities

When we add or subtract the same number from both sides of an inequality, the inequality sign remains unchanged.

Example:

Find the new inequality when:

a) 3 is added to both sides of 4 < 10

b) 4 is subtracted from 7 > 2

Solution:

a) 4 < 10

4 + 3 < 10 + 3

7 < 13

b) 7 > 2

7 – 4 > 2 – 4

3 > – 2

When we multiply or divide the same positive number from both sides of an inequality, the inequality sign remains unchanged.

Example:

Find the new inequality when:

a) 3 < 5 is multiplied both sides by 2

b) 18 > 9 is divided both sides by 3

Solution:

a) 3 < 5

3 × 2 < 5 × 2

6 < 10

b) 18 > 9

18 ÷ 3 > 9 ÷ 3

6 > 3

When we multiply or divide the same negative number from both sides of an inequality, the inequality sign must be reversed . (change < to > and > to <).

Example:

Find the new inequality when:

a) 4 < 11 is multiplied both sides by – 2

b) 30 > –9 is divided both sides by –3

Solution:

a) 4 < 11

4 × (– 2) < 11 × (– 2)

–8 > –22 (reverse the inequality sign)

b) 30 > –9

30 ÷ (–3) > (–9) ÷ (–3)

–10 < 3 (reverse the inequality sign)

The following videos show more examples of solving inequalities:

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