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Verified answer
|x + 2| ≥ |2x -7|(x + 2)^2 ≥ (2x - 7)^2
(x + 2)^2 - (2x - 7)^2 ≥ 0
(x + 2 + 2x - 7) (x + 2 - 2x + 7) ≥ 0
(3x - 5) (-x + 9) ≥ 0
5/3 ≤ x ≤ 9
HP = {5/3 ≤ x ≤ 9}