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

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

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.

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.

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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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:

• 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:

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

Hence, the correct answer is option D.

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Re: If |2x - 7| > 17, which of the following must be true ................ [#permalink]
Why are we not flipping the sign when dividing it by the number before X ?
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Re: If |2x - 7| > 17, which of the following must be true ................ [#permalink]
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Re: If |2x - 7| > 17, which of the following must be true ................ [#permalink]
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