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WE: Supply Chain Management (Energy and Utilities)

Re: How many integers x satisfy |2x + 3 | < 6 ?
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16 Jul 2018, 23:16

1

1

Bunuel wrote:

How many integers x satisfy |2x + 3 | < 6 ?

A. 1

B. 2

C. 6

D. 7

E. 8

Given, \(|2x + 3 | < 6\) Or, \(|x-(\frac{-3}{2})|< 3\) (Dividing both sides of the inequality by 2) Or, \((\frac{-3}{2}-3) < x < (\frac{-3}{2}+3)\) Or, -\(4.5<x<1.5\) So, Possible integer values of x: -4, -3, -2, -1, 0, 1

So, no of integers are 6.

Ans. (C)
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PKN Rise above the storm, you will find the sunshine

Re: How many integers x satisfy |2x + 3 | < 6 ?
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19 Jul 2018, 17:19

Bunuel 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.

Answer: C
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