Inequalities

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Inequalities

by BTGmoderatorRO » Wed Dec 13, 2017 5:51 pm
What inequality represents the condition 1<x<9?

(A) |x|<3
(B) |x+5|<4
(C) |x-1|<9
(D) |-5+x|<4
(E) |3+x|<5

OA is D
Can this question be solved graphically? Expert pls explain the other methods too.Thanks a lot
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by [email protected] » Wed Dec 13, 2017 7:38 pm
Hi Roland2rule,

To start, there's some missing information in this question - it's supposed to state "What inequality represents the condition 1<X<9?"

This question can be solved be TESTing VALUES and eliminating the answer choices that don't match. According to the prompt, X can be any value in the range 1 < X < 9.

IF.... X=8.... then we can eliminate Answers A, B and E.

With the two remaining answers, all of the possible values of X "fit" both inequalities. However, Answer C would include the value X = 9.5 among it's solutions... but that does NOT fit the original range given, so Answer C is NOT the answer.

Final Answer: D

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by GMATGuruNY » Thu Dec 14, 2017 3:53 am
Roland2rule wrote:What inequality represents the condition 1 < x < 9?

(A) |x|<3
(B) |x+5|<4
(C) |x-1|<9
(D) |-5+x|<4
(E) |3+x|<5
|x-y| = the DISTANCE between x and y

The midpoint between 1 and 9 = 5.
The given range implies that x can be any value between 1 (4 places to the LEFT of 5) and 9 (4 places to the RIGHT of 5).
In other words: the distance between x and 5 must be less than 4.
In math terms:
|x-5| < 4.
The expression in blue is the same as the following:
|-5+x| < 4.

The correct answer is D.

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