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# Which of the following statements is equivalent to (8 + 2X < 18 6X < 2

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Math Expert
Joined: 02 Sep 2009
Posts: 43893
Which of the following statements is equivalent to (8 + 2X < 18 6X < 2 [#permalink]

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21 Jun 2016, 02:12
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85% (01:26) correct 15% (02:20) wrong based on 91 sessions

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Which of the following statements is equivalent to $$8 + 2X < 18 - 6X < 23 + 2X$$?

A. 4/5 < X < 2.5.
B. 4/5 < X < 8/5.
C. -5/8 < X < 5/4.
D. 2.5 < X < 3.5.
E. 5 < 8X < 12.
[Reveal] Spoiler: OA

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Re: Which of the following statements is equivalent to (8 + 2X < 18 6X < 2 [#permalink]

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21 Jun 2016, 08:56
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Bunuel wrote:
Which of the following statements is equivalent to $$8 + 2X < 18 - 6X < 23 + 2X$$?

A. 4/5 < X < 2.5.
B. 4/5 < X < 8/5.
C. -5/8 < X < 5/4.
D. 2.5 < X < 3.5.
E. 5 < 8X < 12.

$$8 + 2X < 18 - 6X < 23 + 2X$$

8<18-8x<23 (add -2x on all sides)

-10<-8x<5

10>8x>-5 (multiply by -1 on all sides)

5/4>x>-5/8

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Re: Which of the following statements is equivalent to (8 + 2X < 18 6X < 2 [#permalink]

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22 Jun 2016, 02:04
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Bunuel wrote:
Which of the following statements is equivalent to $$8 + 2X < 18 - 6X < 23 + 2X$$?

A. 4/5 < X < 2.5.
B. 4/5 < X < 8/5.
C. -5/8 < X < 5/4.
D. 2.5 < X < 3.5.
E. 5 < 8X < 12.

8 + 2X < 18 - 6X < 23 + 2X

Taking one inequality at a time,
8 + 2X < 18 - 6X
8X < 10
X < 5/4 - (i)

18 - 6X < 23 + 2X
8X > -5
X > -5/8 - (ii)

Combining (i) and (ii),

-5/8 < X < 5/4

Correct Option: C
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Joined: 18 Jan 2010
Posts: 256
Re: Which of the following statements is equivalent to (8 + 2X < 18 6X < 2 [#permalink]

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22 Jun 2016, 03:59
Bunuel wrote:
Which of the following statements is equivalent to $$8 + 2X < 18 - 6X < 23 + 2X$$?

A. 4/5 < X < 2.5.
B. 4/5 < X < 8/5.
C. -5/8 < X < 5/4.
D. 2.5 < X < 3.5.
E. 5 < 8X < 12.

8+2X< 18 - 6X

2X + 6X < 18 - 8

8X < 10
X < (5/4)

Only C has this option.

[Verify:

18-6X < 23+2X

18-23 < 8 X
-5 < 8X

X > - (5/8) .
Once again this is appearing only in option C]
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Joined: 09 Sep 2013
Posts: 13781
Re: Which of the following statements is equivalent to (8 + 2X < 18 6X < 2 [#permalink]

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26 Jan 2018, 06:06
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: Which of the following statements is equivalent to (8 + 2X < 18 6X < 2   [#permalink] 26 Jan 2018, 06:06
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