Question

What is the solution to the inequality |2x + 3| > 19?

A) x < -11
B) x > 8
C) -11 < x < 8
D) x < -8 or x > 11

Answer 1

The solution to the inequality |2x + 3| > 19 is x < -11 or x > 8.

Step-by-step explanation:

To find the solution to the inequality |2x + 3| > 19, we need to consider two cases: when 2x + 3 is positive and when it is negative.

Case 1: When 2x + 3 > 0, the inequality becomes 2x + 3 > 19. Solving this, we get x > 8.

Case 2: When 2x + 3 < 0, the inequality becomes -(2x + 3) > 19. Simplifying, we have -2x - 3 > 19, which gives us x < -11.

Therefore, the solution to the inequality |2x + 3| > 19 is x < -11 or x > 8. Hence, the correct answer is D) x < -8 or x > 11.