1. Algebra 1
Section 4.3

2. 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.

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

4. ( ) 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

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

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

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

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

9. 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.

10. Homework: pp