Question

Solve the compound inequality 9x ≤-27 or 4x ≥ 36.

A. no solution
B. x ≤ -3 or x ≥ 9
C. all real numbers
D. -3 ≥ x ≤ 9

Answer 1

To solve the compound inequality 9x ≤ -27 or 4x ≥ 36, divide each inequality to solve separately, then combine the solutions as x ≤ -3 or x ≥ 9.

Step-by-step explanation:

To solve the compound inequality 9x ≤-27 or 4x ≥ 36, we need to solve each inequality separately and then combine the solutions. Let's start with the first inequality:

9x ≤ -27

1. Divide both sides of the inequality by 9 to isolate x: x ≤ -3

Now let's solve the second inequality:

4x ≥ 36

1. Divide both sides of the inequality by 4 to isolate x: x ≥ 9

Since we are looking for the combined solutions, we can write the solution to the compound inequality as x ≤ -3 or x ≥ 9. Therefore, the correct answer is B. x ≤ -3 or x ≥ 9.