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

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Founder
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If |3x + 7| ≥ 2x + 12, then which of the following is true? [#permalink]  08 Aug 2018, 16:28
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70% (01:19) correct 29% (01:21) wrong based on 75 sessions
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]  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.

$$-3x - 7 \geq2x + 12$$

$$x \leq-19/5.$$

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Re: If |3x + 7| ≥ 2x + 12, then which of the following is true? [#permalink]  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?
Founder
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Re: If |3x + 7| ≥ 2x + 12, then which of the following is true? [#permalink]  04 Mar 2020, 16:23
Expert's post
See the explanation above. It is perfect.

let me know if you do need further assistance

Regards
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Re: If |3x + 7| ≥ 2x + 12, then which of the following is true? [#permalink]  04 Mar 2020, 18:04
Expert's post
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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Brent Hanneson – Creator of greenlighttestprep.com
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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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