Question

Solve the following absolute value inequality: |x – 9| < 5

A) x<4
B) x>14
C) 4D) x<14

Answer 1

To solve the absolute value inequality |x - 9| < 5, split it into 2 separate inequalities: x - 9 < 5 and -(x - 9) < 5. Solving these yields x < 14 and x > 4. So, the correct answer is x < 14.

Step-by-step explanation:

To solve the absolute value inequality |x - 9| < 5, you can split it into two separate inequalities:

1. x - 9 < 5

2. -(x - 9) < 5

Solving the first inequality, x - 9 < 5, you add 9 to both sides to get x < 14.

Solving the second inequality, -(x - 9) < 5, you multiply both sides by -1 and distribute the negative sign to get x - 9 > -5. Adding 9 to both sides gives x > 4.

Combining the solutions, we have x < 14 and x > 4. Therefore, the correct answer is option D) x < 14.