If |x - 2 | |x + 4| then what is the range of x?

Question

If |x - 2 | > |x + 4| then what is the range of x?

A. x – 4 > 0

B. x < -1

C. x + 2 < 0

D. 3 - x > 0

E. x + 4 > 0

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ManifestDreamMBA · Answer

Thinking of number line, distance of x from 2 is more than distance from x from -4. The mid point is -1, so x must be less than -1 to satisfy the inequality below

Answer B

GMATinsight · Answer

|x - 2 | > |x + 4|

Let's use some logic here

Absolute value of x-2 is greater than absolute value of x+4

which is NEVER possible for positive value of x
i.e. x is Negative (Eliminated Options A, D)

Now, let's check the break-even value i.e. value at which Absolute value of x-2 is EQUAL TO absolute value of x+4

which is true @x = -1 because 2-x = x+4

Now, if you take any value less than -1 such as x=-2 then the above expression is satisfied hence we can conclude that

X < -1