Question

∣x+8∣≤4

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve the inequality, we consider two cases:

Case 1: x + 8 is non-negative

If x + 8 ≥ 0, then ∣x + 8∣ = x + 8.
Substituting this into the inequality, we have x + 8 ≤ 4.
Subtracting 8 from both sides, we get x ≤ -4.

Case 2: x + 8 is negative

If x + 8 < 0, then ∣x + 8∣ = -(x + 8).
Substituting this into the inequality, we have -(x + 8) ≤ 4.
Multiplying both sides by -1, we get x + 8 ≥ -4.
Subtracting 8 from both sides, we get x ≥ -12.

Combining the solutions from both cases, we have:
x ≤ -4 or x ≥ -12.