Question

Solve and find the two solutions.
3|x+4|-8>=1

Answer 1

To solve the inequality 3|x+4|-8≥1, we split into two cases based on the absolute value. Case 1 yields x ≥ -1, and Case 2 yields x ≤ -7. The solution set is the union of both cases.

Step-by-step explanation:

To solve the inequality 3|x+4|-8≥1, we must consider the two cases for the absolute value function.

Case 1: x + 4 ≥0

In this case, |x+4| = x + 4. Our inequality becomes:

3(x + 4) - 8 ≥ 1

3x + 12 - 8 ≥ 1

3x + 4 ≥ 1

3x ≥ -3

x ≥ -1

Case 2: x + 4 < 0

In this case, |x+4| = -(x + 4). Our inequality becomes:

3(-x - 4) - 8 ≥ 1

-3x - 12 - 8 ≥ 1

-3x - 20 ≥ 1

-3x ≥ 21

x ≤ -7

Combining the two cases, our solution set is x ≥ -1 or x ≤ -7.