If |2x - 7| > 17, which of the following must be true?

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If |2x - 7| > 17, which of the following must be true?

A. -5 < x < 0
B. 0 < x < 12
C. -5 < x < 12
D. x < -5 or x > 12
E. x < -12 or x > 5

Answer: D
Source: E-gmat

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BTGModeratorVI wrote:
Thu Aug 20, 2020 7:14 am
If |2x - 7| > 17, which of the following must be true?

A. -5 < x < 0
B. 0 < x < 12
C. -5 < x < 12
D. x < -5 or x > 12
E. x < -12 or x > 5

Answer: D
Source: E-gmat
----ASIDE-----------------------
When solving inequalities involving ABSOLUTE VALUE, there are 2 things you need to know:
Rule #1: If |something| < k, then –k < something < k
Rule #2: If |something| > k, then EITHER something > k OR something < -k
Note: these rules assume that k is positive

-----ONTO THE QUESTION----------

GIVEN: |2x - 7| > 17
Rule #2 tells us that EITHER 2x - 7 > 17 OR 2x - 7 < -17

Take: 2x - 7 > 17
Add 7 to both sides: 2x > 24
Solve: x > 12

Take: 2x - 7 < -17
Add 7 to both sides: 2x < -10
Solve: x < -5

So, either x > 12 or x < -5

Answer: D
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BTGModeratorVI wrote:
Thu Aug 20, 2020 7:14 am
If |2x - 7| > 17, which of the following must be true?

A. -5 < x < 0
B. 0 < x < 12
C. -5 < x < 12
D. x < -5 or x > 12
E. x < -12 or x > 5

Answer: D
Source: E-gmat
Sometimes, the quickest solution to this kind of question involves testing the answer choices

Scan the answer choices
Notice that some answer choices say that x = 1 is a solution, and some say x = 1 is NOT a solution.
So, let's test x = 1
Plug it into the original inequality to get:|2(1) - 7| > 17
Simplify to get: |-5| > 17
NOT true
So, x = 1 is NOT a solution to the inequality.
We can ELIMINATE B and C because they say that x = 1 IS a solution.

Scan the remaining answer choices
Notice that some answer choices say that x = -1 is a solution, and some say x = -1 is NOT a solution.
So, let's test x = -1
Plug it into the original inequality to get:|2(-1) - 7| > 17
Simplify to get: |-9| > 17
NOT true
So, x = -1 is NOT a solution to the inequality.
We can ELIMINATE A because it says x = -1 IS a solution.

We're down to answer choices D or E.
E says x = 6 is a solution, and D says x = 6 is NOT a solution.
So, let's test x = 6
Plug it into the original inequality to get:|2(6) - 7| > 17
Simplify to get: |5| > 17
NOT true
We can ELIMINATE E because it says x = 6 IS a solution.

Answer: D

NOTE: With this particular question, testing the answer choices is a slower approach. However, when solving questions of this nature, the approach is still worth considering, especially with more complex inequalities.


Cheers,
Brent
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BTGModeratorVI wrote:
Thu Aug 20, 2020 7:14 am
If |2x - 7| > 17, which of the following must be true?

A. -5 < x < 0
B. 0 < x < 12
C. -5 < x < 12
D. x < -5 or x > 12
E. x < -12 or x > 5
|2x - 7| > 17 is clearly satisfied if x=100.
Eliminate A, B and C, whose ranges do not include x=100.

D: x>12
E: x>5

Test a value BETWEEN 5 AND 12.
If x=10, then |2x - 7| > 17 is NOT satisfied.
Since x=10 is not a valid solution, eliminate E.

The correct answer is D.
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