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If |x| < 20 and |x – 8| > |x + 4|, which of the foll

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by Vincen » Thu Nov 02, 2017 8:45 am
If |x| < 20 and |x – 8| > |x + 4|, which of the following expresses the allowable range for x?

(A) –12 < x < 12

(B) –20 < x < 2

(C) –20 < x < –12 and 12 < x < 20

(D) –20 < x < –8 and 4 < x < 20

(E) –20 < x < –4 and 8 < x < 20

The OA is B.

I understand the meaning of the first inequality, but the second one confused me.

Experts, may you give me some help? How can I solve this PS question?
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by [email protected] » Fri Nov 03, 2017 1:40 pm
Hi Vincen,

We're told that |X| < 20 and |X - 8| > |X + 4|. We're asked for the range of values for X. Since the answer choices are all ranges, we can use them 'against' the prompt and TEST VALUES.

To start, let's TEST an 'easy' value for X to see if it 'fits' what we're told:
Could X=0?
|0| is less than 20; |0-8| is greater than |0+4|.
Thus X=0 IS a possible value. Eliminate Answers C, D and E.

With the two remaining answers, we should look to TEST a value that is in one of the ranges but NOT the other.
Could X=10?
|10| is less than 20; |10-8| is NOT greater than |10+4|.
Thus X=10 is NOT a possible value. Eliminate Answer A

Final Answer: B

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