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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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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]
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.

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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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