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Bunuel
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If 2|2 –x| = 5, what is the sum of all the possible values for x ? 21 Oct 2021, 08:45
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D
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If 2|2 –x| = 5, what is the sum of all the possible values for x ?

A. 1/2
B. 2
C. 5/2
D. 4
E. 5
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D
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If 2|2 –x| = 5, what is the sum of all the possible values for x ? Updated on: 21 Oct 2021, 10:23
Originally posted by BrentGMATPrepNow on 21 Oct 2021, 09:35.
Last edited by BrentGMATPrepNow on 21 Oct 2021, 10:23, edited 1 time in total.
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Bunuel
If 2|2 –x| = 5, what is the sum of all the possible values for x ?

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

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
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If 2|2 –x| = 5, what is the sum of all the possible values for x ? 21 Oct 2021, 09:53
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|2 - x| = (5/2)

- (2 - x) = (5/2) or (2 - x) = (5/2)
(x - 2) = (5/2) or (2 - x) = 5/2
x = [(5/2) + 2] or x = [2- (5/2)]
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

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If 2|2 –x| = 5, what is the sum of all the possible values for x ? 21 Oct 2021, 09:54
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Sum of all the possible values of X

Property 1: [A - B] = [B -A]

Thus we can rearrange the equation:

2 * [X - 2] = 5

Divide both sides of the equation by 2

[X - 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

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If 2|2 –x| = 5, what is the sum of all the possible values for x ? 21 Oct 2021, 09:55
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BrentGMATPrepNow
Bunuel
If 2|2 –x| = 5, what is the sum of all the possible values for x ?

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

None of the above.
If 2|2–x| = 5, then x = -0.5 or x = 4.5

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

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If 2|2 –x| = 5, what is the sum of all the possible values for x ? 21 Oct 2021, 10:24
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ktzsikka
Why none of the above. Shouldn't it be option D=4.
As \(-0.5+4.5=4.0\)

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

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If 2|2 –x| = 5, what is the sum of all the possible values for x ? 21 Oct 2021, 10:31
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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
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If 2|2 –x| = 5, what is the sum of all the possible values for x ? 23 Oct 2021, 01:42
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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

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

A. 1/2
B. 2
C. 5/2
D. 4
E. 5
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If 2|2 –x| = 5, what is the sum of all the possible values for x ? 23 Oct 2021, 01:55
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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

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If 2|2 –x| = 5, what is the sum of all the possible values for x ? Updated on: 18 Oct 2024, 21:29
Originally posted by BrushMyQuant on 28 May 2022, 03:22.
Last edited by BrushMyQuant on 18 Oct 2024, 21:29, edited 1 time in total.
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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
image.JPG [ 18.85 KiB | Viewed 4821 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

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If 2|2 –x| = 5, what is the sum of all the possible values for x ? 28 May 2022, 11:42
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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.
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If 2|2 –x| = 5, what is the sum of all the possible values for x ? 16 Jun 2025, 16:24
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