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

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

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.

Answer: D

Why are we not flipping the sign when dividing it by the number before X ?

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