Objective #5: Solve Compound Inequalities Compound Inequality: 2 inequalities joined by the word “and” or “or”. To solve one, you have to solve each part. The solution to an “and” inequality are the values that make both inequalities true The solution to an “or” inequality are the values that make either inequality true An “and” inequality can be written 2 ways. For example, “x is greater than or equal to -4 and less than 3” can be written as x ≥ -4 and x < 3 OR -4 ≤ x < 3

2 methods for solving an “and” inequality: Ex. Solve 8 < 3x − 7 ≤ 23 Method 1: solve separately 3x – 7 > 8 and 3x – 7 ≤ 23 3x > 15 and 3x ≤ 30 X > 5 and x ≤ 10 Method 2: solve both together 8 < 3x − 7 ≤ 23 *add 7 to each part* 15 < 3x ≤ 30 *divide each part by 3* 5 < x ≤ 10