Question

| 2 +r | ≥ 3 (lines are absolute value)

Answer 1

r ≤ -5 and r ≥ 1

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