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