If 2|2 –x| = 5, what is the sum of all the possible values for x ?

Question

A. 1/2
B. 2
C. 5/2
D. 4
E. 5

BrentGMATPrepNow · Accepted Answer

Wow, I certainly misread that question!! 
I first read it as "What is the value of x?"

Take 2|2–x| = 5
Divide both sides of the equation by 2 to get: |2 - x| = 2.5
This means that either 2 - x = 2.5, or 2 - x = -2.5
 
If 2 - x = 2.5, then x =  -0.5 
If 2 - x = -2.5, then x =  4.5

So the sum of the solutions = ( -0.5 ) +  4.5  =  4

Answer: D

100mitra · Answer

|2 - x| = (5/2)

- (2 - x) = (5/2) or (2 - x) = (5/2)
 (x - 2) = (5/2) or (2 - x) = 5/2
 x =   or x =  
 x = (9/2) or x = -(1/2)

Possible value of x {-1/2 , 9/2}
Aum of possible value of 
= (-1/2) + 9/2 
= (9/2) - (1/2) 
= (8/2) 
= 4 
 = Option D

Posted from my mobile device

Fdambro294 · Answer

Sum of all the possible values of X

Property 1:   =

Thus we can rearrange the equation:

2 *   = 5

Divide both sides of the equation by 2

= 2.5

Translation: “on the number line, The distanced from X to +2 is exactly 2.5 units in both directions.”

X = 4.5

Or

X = -0.5

Sum of all the possible values of X:

(4.5) + (-0.5) = 4

Answer D
4

Posted from my mobile device

ktzsikka · Answer

Why none of the above. Shouldn't it be option D=4.
As  -0.5+4.5=4.0

Posted from my mobile device

BrentGMATPrepNow · Answer

You're absolutely right. I totally misread the question. 
I have edited my response accordingly.

Kudos for you!!

Kinshook · Answer

Asked: If 2|2 –x| = 5, what is the sum of all the possible values for x ?

|x-2| = 2.5
x = 4.5 or -.5
Sum of all the possible values of x = 4.5 + (-.5) = 4

IMO D

Archit3110 · Answer

2|2 –x| = 5 
value of x
4-2x=5
-2x=1
x=-1/2
and
-4+2x=5
2x=9
x=9/2

sum of -1/2+9/2 ; 8/2 ; 4
option D

yoginipatil12 · Answer

Option D
2|2 –x| = 5
value of x
4-2x=5
-2x=1
x=-1/2
and
-4+2x=5
2x=9
x=9/2

sum of -1/2+9/2 ; 8/2 ; 4
option D

Posted from my mobile device

BrushMyQuant · Answer

Given that 2|2 –x| = 5 and we need to find the sum of all the possible values for x

2|2 –x| = 5
=> | 2-x| = \(\frac{5}{2}\) = 2.5

Let's solve the problem using three methods

Method 1: Substitution

|2-x| = 2.5
=> 2-x = ± 2.5
=> x can be -0.5 or 4.5

Sum of all possible values of x = -0.5 + 4.5 = 4

Method 2: Algebra

2|2 –x| = 5
=> |2-x| = \(\frac{5}{2}\) = 2.5

Watch this video to Master Absolute Value

As we have \|2-x\| in the equation so we will have two cases
-Case 1: 2-x ≥ 0 => x ≤ 2 => \|2-x\| = 2-x => 2-x = 2.5 => x = -0.5 But condition was x ≤ 2 and -0.5 ≤ 2 => x = -0.5 is a SOLUTION	-Case 2: 2-x ≤ 0 => x ≥ 2 => \|2-x\| = -(2-x) = x - 2 => x - 2 = 2.5 => x = 4.5 But condition was x ≥ 2 and 4.5 ≥ 2 => x = 4.5 is a SOLUTION

=> Sum of all possible values of x = -0.5 + 4.5 = 4

Method 3: Graphical Method

|2-x| = 2.5
|2 -x | means the distance between x and 2
|2-x| = 2.5 => Distance between x and 2 = 2.5

Attachment:

image.JPG [ 18.85 KiB | Viewed 5899 times ]

So, x can be 2.5 to the left or to the right of 2
=> x = -0.5 or x = 4.5

So, Answer will be D
Hope it helps!

Watch the following video to learn How to Solve Absolute Value Problems

GMATWhizTeam · Answer

It is given that 2 | 2 -x | = 5.

The equation can be reorganised to bring all the constants on to one side. Therefore, 
|2 – x| =  \frac{5 }{ 2} .

This means the expression (2 – x) =  \frac{ 5 }{ 2}  or (2 – x) = -  \frac{5 }{ 2}

When (2 – x) =  \frac{5 }{ 2} , x = -  \frac{1 }{ 2} .

When (2 – x) = -  \frac{5 }{ 2} , x =  \frac{9 }{ 2} .

The sum of the values of x =  \frac{9 }{ 2}  –  \frac{1}{ 2}  =  \frac{8 }{ 2}  = 4

The correct answer option is D.

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

If 2|2 –x| = 5, what is the sum of all the possible values for x ?

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

If 2|2 –x| = 5, what is the sum of all the possible values for x ?

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards