\(|3x+7| \geq{2x+12}\) 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

\(|3x+7| \geq{2x+12}\) is true when \(x \geq 5\) or \(x \leq \frac{19}{5}\). Which is option D.

P.S. Does the question is worded

as you written? Does it say "which of the following is x value"?