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

Question

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

BrentGMATPrepNow · Accepted Answer

----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

Chethan92 · Answer

If |x| > a Then x > a if x > 0 Or -x > a if x< 0 i.e x < -a Back to the question |2x - 7| > 17 2x-7 > 17 If x > 7/2 Or 2x-7 < -17 Solving gives x > 12 or x < -5. D is the answer .

BrentGMATPrepNow · Answer

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

EgmatQuantExpert · Answer

Solution

Given:

• We are given an inequality, |2x - 7| > 17
To find:

• We need to find out the values of x, which satisfies the given inequality
Approach and Working:
Let’s remove the modulus first, by squaring the inequality on both sides

 (x – 12)(x + 5) > 0

Approach 1: Wavy-line method

The zero points are {-5, 12}, and the wavy-line will be as follows:

Approach 2: Number-line method

The zero points are {-5, 12}, and the number-line will be as follows:

Therefore, (x – 12)(x + 5) is positive for x < -5 or x > 12

Hence, the correct answer is option D.

Answer: D

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

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