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If |3x + 7| ≥ 2x + 12, then which of the following is true?

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If |3x + 7| ≥ 2x + 12, then which of the following is true? [#permalink] New post 08 Aug 2018, 16:28
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If \(|3x + 7| ≥ 2x + 12\), then which of the following is true?

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

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

C. \(x \geq 5\)

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

E. \(\frac{-19}{5} \leq x \leq 5\)


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[Reveal] Spoiler: OA

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Re: If |3x + 7| ≥ 2x + 12, then which of the following is true? [#permalink] New post 09 Aug 2018, 14:06
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Carcass wrote:
If \(|3x + 7| ≥ 2x + 12\), then which of the following is true?

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

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

C. \(x \geq 5\)

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

E. \(\frac{-19}{5} \leq x \leq 5\)


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For absolute value there will be 2 cases all time.

Case 1 : when 3x + 7 is positive.

\(3x + 7 \geq2x + 12\)

\(x \geq5\)


Case 2: When 3x + 7 is negative.

\(-3x - 7 \geq2x + 12\)

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

The best answer is D.
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Re: If |3x + 7| ≥ 2x + 12, then which of the following is true? [#permalink] New post 04 Mar 2020, 14:34
For some reason I keep getting X less than or equal to -19/5 when I make the right side negative and add the variables to get +5. Why does thi shappen?
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Re: If |3x + 7| ≥ 2x + 12, then which of the following is true? [#permalink] New post 04 Mar 2020, 16:23
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See the explanation above. It is perfect.

let me know if you do need further assistance

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Re: If |3x + 7| ≥ 2x + 12, then which of the following is true? [#permalink] New post 04 Mar 2020, 18:04
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NickBass wrote:
For some reason I keep getting X less than or equal to -19/5 when I make the right side negative and add the variables to get +5. Why does thi shappen?


If you show the steps you take to reach -19/5, we can probably sort things out.

Cheers,
Brent
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Re: If |3x + 7| ≥ 2x + 12, then which of the following is true?   [#permalink] 04 Mar 2020, 18:04
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