Bunuel wrote:

If x is an integer, what is the value of x such that |-5x + 7| is minimized?

A. 0

B. 1

C. 2

D. 3

E. 4

Responding to a pm:

**Quote:**

I am stuck b/w A and B. If they are looking for minimum value when you plug in A you get + / - 7 and with B you get +-2. So shouldn't the answer be A given that -7 is less than -2. (or minimum value.)??

We are looking for the minimum value of |-5x + 7|.

If we put x = 0, |-5x + 7| = |-5*0 + 7| = 7

Note that |7| is NOT 7 or -7.

|7| and |-7| both are equal to 7 ONLY

If we put x = 1, |-5x + 7| = |-5*1 + 7| = 2 ONLY

You are getting confused with the definition of absolute values:

|x| = x if x >= 0

|x| = -x if x < 0

So if x = 5, |x| = x = 5 (because x > 0)

If x = -5, |x| = -x = - (-5) = 5 (because x < 0)

That is the whole point of absolute value: It is never negative. It is the distance in physical terms so it cannot be negative.

_________________

Karishma

Veritas Prep GMAT Instructor

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