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# How many integers x satisfy

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How many integers x satisfy [#permalink]  16 Jul 2018, 00:00
Expert's post
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Question Stats:

55% (00:51) correct 44% (00:44) wrong based on 29 sessions
How many integers $$x$$ satisfy $$|2x + 3 | < 6$$

A. 1

B. 2

C. 6

D. 7

E. 8
[Reveal] Spoiler: OA

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Re: How many integers x satisfy [#permalink]  17 Jul 2018, 07:41
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Carcass wrote:
How many integers $$x$$ satisfy $$|2x + 3 | < 6$$

A. 1

B. 2

C. 6

D. 7

E. 8

As we are dealing with modulus we have to consider both negative and positive aspects.

Case 1 : when 2x + 3 is positive.

2x + 3 < 6

x < 1.5.

Case 2: when 2x + 3 is negative .

-2x -3 < 6
x > -4.5.

So,

-4.5 <x<1.5.

There are 6 values in total : -4, -3 , -2, -1, 0 , 1.

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Re: How many integers x satisfy [#permalink]  19 Jul 2018, 15:59
Expert's post
Carcass wrote:
How many integers $$x$$ satisfy $$|2x + 3 | < 6$$

A. 1

B. 2

C. 6

D. 7

E. 8

Recall that if k is a positive constant and |ax + b| < k, then -k < ax + b < k. So we can solve the given inequality by removing the absolute value sign and change it to the following double inequality:

-6 < 2x + 3 < 6

-9 < 2x < 3

-9/2 < x < 3/2

-4.5 < x < 1.5

The integers x can be are: -4, -3, -2, -1, 0, and 1. So there are 6 integers that satisfy the inequality.

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Re: How many integers x satisfy   [#permalink] 19 Jul 2018, 15:59
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