$|3x+7| \geq{2x+12}$ which of the following is x value:

(A) $x\leq{-\frac{19}{5}}$

(B) $x\geq{-\frac{19}{5}}$

(C) $x\leq{5}$

(D) $x\leq{-\frac{19}{5}}$ or $x\geq{5}$

(E) $\frac{-19}{5} < x < 5$

After solving the inequality I got the two answers X >=5 and X <= -19/5. but since this is an absolute question I checked each answer by plug in the two possible answers in the original equation and I found that x <= -19/5 is an erroneous value, so I chose answer choice (C) as the correct answer, but the book gives (D) as the correct answer. what I'm missing here

$|3x+7| \geq{2x+12}$ which of the following is x value: