EgmatQuantExpert wrote:

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

Sometimes, the quickest solution to this kind of question involves

testing the answer choicesScan 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 =

1Plug 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 =

-1Plug 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 =

6Plug 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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