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Re: Absolute Inequality [#permalink]
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I do not know why is D the answer unless the X takes negative values.

For positive values the answer is E.

Waiting expert.
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Re: |3x+7| >= 2x+12 which of the following is x value: [#permalink]
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f4h6 wrote:
\(|3x+7| \geq{2x+12}\) 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 exactly as you written? Does it say "which of the following is x value"?
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Re: |3x+7| >= 2x+12 which of the following is x value: [#permalink]
f4h6 wrote:
\(|3x+7| \geq{2x+12}\) which of the following is x value:



Here we have to consider both positive and negative values of (3x +7) since it under |3x+7|

Considering +ve we get -

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

or \(3x \geq 2x + 5\)

or \(x \geq 5\)


Now considering negative

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

or \(3x +7 \leq -(2x+12)\)

or \(3x +7 \leq -2x-12\)

or \(5x \leq -19\)

or \(x \leq -19/5\).

Therefore \(x \geq 5\) or \(x \leq -19/5\)

Hence option D
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Re: |3x+7| >= 2x+12 which of the following is x value: [#permalink]
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