∣x+10∣≤6

To solve for x in the inequality |x + 10| ≤ 6, we need to consider two cases:

Case 1: x + 10 is non-negative (x + 10 ≥ 0)
In this case, the inequality simplifies to x + 10 ≤ 6
Subtracting 10 from both sides:
x ≤ -4

Case 2: x + 10 is negative (x + 10 < 0)
In this case, the absolute value inequality becomes -(x + 10) ≤ 6
Simplifying, we get -x - 10 ≤ 6
Adding 10 to both sides and multiplying by -1:
-x ≤ 16
x ≥ -16

Putting both cases together, the solution to the inequality |x + 10| ≤ 6 is -16 ≤ x ≤ -4.