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

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Joined: 02 Sep 2009
Posts: 60627
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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25% (medium)

Question Stats:

76% (01:27) correct 24% (01:24) wrong based on 113 sessions

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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

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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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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
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 3682 times ]

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

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

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28 Nov 2019, 07:47
Top Contributor
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

GIVEN: 4 < 7 - 2x < 12
Subtract 7 from all sides to get: -3 < -2x < 5
Divide all sides by -2 to get: 1.5 > x > -2.5 [ since I divided both sides of the inequality by a NEGATIVE value, I had to REVERSE the direction of the inequality symbols]

If x is an INTEGER that is BETWEEN -2.5 and 1.5, then x CAN equal -2, -1, 0 or 1 (4 options)

Cheers,
Brent

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Re: If 4 < 7 - 2x < 12, how many integer values of x are there?   [#permalink] 28 Nov 2019, 07:47
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