What+does+a+compound+inequality+look+like?+How+is+this+different+from+a+regular+inequality?+Give+a+few+examples.+Set+3

Which of the following are compound inequalities? Simplify the compound inequalities, when possible. Also, Explain how you know when something is a compound inequality and something is a regular inequality.

1. 3x - 18 < 6 or 12x - 144 > 0

2. 8x + 7 ≤ 12

3. 75 < 5x + 10 ≤ 195

4. 5 ≤ x < 8.5

5. 12x + 75 > 6x + 4

6. x ≥ 7 or x < -12

7. x > 0 and -5x >- 25

Answer: 1, 3, 4, 6, and 7 are compound inequalities. You can deduce this by checking to see if the inequality has multiple parts. For example, a betweenness is a compound inequality because it has terms before, inside, and after the > sign. The other kind of compound inequality --an and/or statement-- is compound because it can be split apart into two inequalities.

1. 3x - 18 < 6 or 12x - 144 > 0 3x 144
 * x 12**

3. 75 < 5x + 10 ≤ 195 65<5x≤185
 * 13 0 and -5x >- 25 x>0 and x<5
 * 0<x<5**