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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 ................  [#permalink]

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New post 31 Oct 2018, 04:30
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

79% (01:16) correct 21% (01:24) wrong based on 127 sessions

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Re: If |2x - 7| > 17, which of the following must be true ................  [#permalink]

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New post 31 Oct 2018, 04:49
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.
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Re: If |2x - 7| > 17, which of the following must be true ................  [#permalink]

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New post 31 Oct 2018, 06:33
Top Contributor
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

----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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Re: If |2x - 7| > 17, which of the following must be true ................  [#permalink]

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New post 31 Oct 2018, 06:42
Top Contributor
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 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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Re: If |2x - 7| > 17, which of the following must be true ................  [#permalink]

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New post 02 Nov 2018, 04:55

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

    • Squaring the given inequality on both sides, gives,
      o \((2x – 7)^2 > 17^2\)
      o Implies, \(4x^2 – 28x + 49 > 289\)
      o \(4x^2 – 28x - 240 > 0\)
      o Taking 4 out, we get, \(x^2 – 7x - 60 > 0\)
      o Factorising the quadratic expression, we can write the above inequality as,
         (x – 12)(x + 5) > 0

Approach 1: Wavy-line method

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

Image

    • The expression will be positive in the regions, x < -5 or x > 12

Approach 2: Number-line method

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

Image

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

Hence, the correct answer is option D.

Answer: D

Image

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Re: If |2x - 7| > 17, which of the following must be true ................   [#permalink] 02 Nov 2018, 04:55
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