Final answer:
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.