Question

Solve the following inequality algebraically: |x + 4| > 11

A) x < -15 or x > 7
B) x < 7 or x > -15
C) x < -7 or x > 15
D) x < 15 or x > -7

Answer 1

To solve the inequality |x + 4| > 11 algebraically, considere two cases: when the expression inside the absolute value is positive and when it is negative. The solution is x < -15 or x > 7.

Step-by-step explanation:

To solve the inequality |x + 4| > 11 algebraically, we need to consider two cases: when the expression inside the absolute value is positive and when it is negative.

Case 1: (x + 4) > 11

Solving this equation, we get x > 7.

Case 2: -(x + 4) > 11

Solving this equation, we get x < -15.

Combining the two cases, the solution is x < -15 or x > 7.