Please help, got part way through it. Looking for x on one side number on the other.

x ≥ 0                   or          x ≤ -3

Step-by-step explanation:

- | 3+2x| +1 ≤ -2

Subtract 1 from each side

- | 3+2x| +1-1 ≤ -2-1

- | 3+2x|  ≤ -3

Divide each side by -1, remembering to flip the inequality

- | 3+2x| / -3 ≥ -3/-1

| 3+2x| ≥ 3

When we have absolute values, we get 2 solutions, one positive and one negative ( remember to flip  the inequality when taking the negative)

3+2x ≥ 3     or       3+2x ≤ -3

Subtract 3 from each side

3-3+2x ≥ 3-3  or          3-3+2x ≤ -3-3

2x ≥ 0                or             2x ≤ -6

Divide each side by 2

2x/2 ≥ 0/2          or           2x/2 ≤ -6/2

x ≥ 0                   or          x ≤ -3