∣x+10∣≤4

This inequality can be solved by breaking it down into two cases:

Case 1: x + 10 ≥ 0

In this case, the absolute value sign can be removed, giving us x + 10 ≤ 4.

Subtracting 10 from both sides, we have x ≤ -6.

Case 2: x + 10 < 0

In this case, the absolute value sign can be removed and the inequality is multiplied by -1, giving us -(x + 10) ≤ 4.

Expanding and simplifying, we have -x - 10 ≤ 4.

Adding x and 10 to both sides, we have x ≥ -14.

Putting the two cases together, the solution to the inequality is -14 ≤ x ≤ -6.