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# If 4 < 7 - 2x < 12, how many integer values of x are there?

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Math Expert
Joined: 02 Sep 2009
Posts: 44290
If 4 < 7 - 2x < 12, how many integer values of x are there? [#permalink]

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21 Oct 2016, 00:27
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If 4 < 7 - 2x < 12, how many integer values of x are there?

A. 6
B. 4
C. 2
D. 1
E. 0
[Reveal] Spoiler: OA

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Posts: 2016
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If 4 < 7 - 2x < 12, how many integer values of x are there? [#permalink]

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21 Oct 2016, 01:05
Bunuel wrote:
If 4 < 7 - 2x < 12, how many integer values of x are there?

A. 6
B. 4
C. 2
D. 1
E. 0

4 < 7 - 2x < 12

4-7 <- 2x < 12-7

-3 <- 2x < 5

3 > 2x > -5

3/2 > x > -5/2

x may be -2, -1, 0, 1

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Joined: 11 Jul 2016
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Re: If 4 < 7 - 2x < 12, how many integer values of x are there? [#permalink]

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21 Oct 2016, 07:46
Bunuel wrote:
If 4 < 7 - 2x < 12, how many integer values of x are there?

A. 6
B. 4
C. 2
D. 1
E. 0

4 < 7 - 2x < 12

Case 1
4 < 7 - 2x

x<3/2 ........(1)

Case 2
7 - 2x < 12

-5/2 <x .......(2)

Plot this on a number line

-5/2 <x < 3/2

Integer values can be : -2 , -1 , 0 , 1

Hence B

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Re: If 4 < 7 - 2x < 12, how many integer values of x are there? [#permalink]

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21 Oct 2016, 09:19
1
KUDOS
Bunuel wrote:
If 4 < 7 - 2x < 12, how many integer values of x are there?

A. 6
B. 4
C. 2
D. 1
E. 0

4 -7 < - 2x < 12 - 7

Or, - 3 < - 2x < 5

Or, - 3/-2 > x > -5/2

Or, $$- 2 \frac{1}{2}$$ > $$x$$ > $$1 \frac{1}{2}$$

Now , form a number line -
Attachment:

MathWarehouse-number-line.gif [ 5.49 KiB | Viewed 1628 times ]

So, There are four number -2 , -1 , 0 , 1

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Joined: 09 Sep 2013
Posts: 6532
Re: If 4 < 7 - 2x < 12, how many integer values of x are there? [#permalink]

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11 Mar 2018, 13:28
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: If 4 < 7 - 2x < 12, how many integer values of x are there?   [#permalink] 11 Mar 2018, 13:28
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