Question

Solve the absolute value inequality: |x + 12| + 5 < 27

a) x < 10
b) x > 10
c) -22 < x < 10
d) x < -22 or x > 10

Answer 1

To solve the absolute value inequality |x + 12| + 5 < 27, subtract 5 from both sides, split the inequality into two separate cases, solve each case separately, and combine the solutions.

Step-by-step explanation:

To solve the absolute value inequality |x + 12| + 5 < 27, we isolate the absolute value term by subtracting 5 from both sides: |x + 12| < 22. Next, we split the inequality into two separate cases: x + 12 < 22 and x + 12 > -22. Solving each case separately, we find that x < 10 and x > -34. Combining the solutions, we get x < 10 or x > -34. Therefore, the correct answer is option d) x < -22 or x > 10.