If |x| = 5x - 16, find sum of all possible values of x.

Question

A. 20

B. 0

C. 4

D. -4

E.  \frac{20}{3}

Nirmesh83 · Answer

If x>0; 4x= 16; x= 4
If x<0 ; 6x=16; x= 8/3 not a solution since x<0
Therefore sumnof all solutions of x is 4

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Catman · Answer

Case I. when x>0 
x=5x-16
x=4

Case II when x<0
-x=5x-16
x=8/3 but x should be less than 0, so not possible.

x=4 only solution and sum is 4.

BrushMyQuant · Answer

↧↧↧ Detailed Video Solution to the Problem ↧↧↧

https://www.youtube.com/watch?v=-GbYo7fwAL4

|x|=5x-16 and we need to find sum of all possible values of x

|x|=5x-16

Let's open the absolute value using two cases

Opening Absolute Value using |x| = x when x≥0 and |x| = -x when x ≤ 0 
 
    -  x ≥ 0

=> |x| = x
=> x = 5x - 16
=> 4x = 16
=> x =  \frac{16}{4}  = 4
And 4 > 0
=> x = 4 is a solution  
 
   -  x ≤ 0

=> |x| = -x
=> -x = 5x - 16
=> 6x = 16
=> x =  \frac{16}{6}  =  \frac{8}{3} 
But  \frac{8}{3}  is NOT < 0
=> x =  \frac{8}{3}  is NOT a solution

=> Sum of all the solutions = 4

So,  Answer will be C 
Hope it helps!

Watch the following video to MASTER Absolute Values

https://www.youtube.com/watch?v=huFiBk8PaGY

bumpbot · Answer

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If |x| = 5x - 16, find sum of all possible values of x.

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Opening Absolute Value using \|x\| = x when x≥0 and \|x\| = -x when x ≤ 0
-x ≥ 0 => \|x\| = x => x = 5x - 16 => 4x = 16 => x = \(\frac{16}{4}\) = 4 And 4 > 0 => x = 4 is a solution	-x ≤ 0 => \|x\| = -x => -x = 5x - 16 => 6x = 16 => x = \(\frac{16}{6}\) = \(\frac{8}{3}\) But \(\frac{8}{3}\) is NOT < 0 => x = \(\frac{8}{3}\) is NOT a solution

GMAT Problem Solving (PS) Questions

If |x| = 5x - 16, find sum of all possible values of x.

Prep Toolkit

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