Question

Solve the inequality.x + 3 + 2 ≤ 4[?] ≤ x ≤ [ ]

Answer 1

We are to solve the inequality:

|x + 3| + 2 ≤ 4

First let's subtract 2 from both sides

|x + 3| + 2 - 2 ≤ 4 - 2

|x + 3| ≤ 2

Apply absolute rule: if |u| ≤ a, a > 0 then -a ≤ u ≤ a

-2 ≤ x + 3 ≤ 2

x + 3 ≥ -2 and x + 3 ≤ 2

x ≥ -5 and x ≤ -1

-5 ≤ x ≤ -1