Answer:
r ≤ -5 and r ≥ 1
Step-by-step explanation:
The solution has two parts:
1) that derived from | 2 +r | ≥ 3 when (2 + r) is already positive. Then:
2 + r ≥ 3, or r ≥ 1
and
that derived from | 2 +r | ≥ 3 when (2 + r) is negative. If (2 + r) is negative, then
|(2 + r)| = -(2 + r) = -2 -r, which is ≥ 3. Therefore, -2 -r ≥ 3, or -r ≥ 5. To solve this for r, divide both sides by -1 and reverse the direction of the inequality sign: r ≤ -5
