Algebra 1 Section 4.3

Solving Inequalities The process of solving inequalities is similar to the process of solving equations. Remember to reverse the inequality symbol when multiplying or dividing by a negative number.

Example 1 Solve 3x + 5 > 20. 3x > 15 > 3 3x 15 x > 5

( ) Example 2 Solve - + 8 ≥ 12. 3 x - ≥ 4 3 x -3 3 x - -3(4) ≤ ≥ - ≥ 4 3 x ( ) -3 3 x - -3(4) ≤ ≥ x ≤ -12

Example 3 Solve 4x – 3(2 + 2x) > 10. 4x – 6 – 6x > 10 < >

Example 4 Solve x + 4 ≥ 5(x + 6) – 2x. x + 4 ≥ 5x + 30 – 2x

( ) Example 5 Length = l Width = 2 l + 5 2l + 2w ≤ 60 2l + 2 ≤ 60 2 l ( ) 2 l + 5 2l + l + 10 ≤ 60

Example 5 2l + l + 10 ≤ 60 3l + 10 ≤ 60 3l ≤ 50 l ≤ 16⅔

Example 5 l ≤ 16⅔ The length is at most 16⅔ ft, or 16 ft 8 in. The width is at most half the length plus 5, or 13 ft 4 in.

Homework: pp. 154-156