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Bunuel
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If |2x − 5| = 25 − x, what is the sum of the two possible values of x? 10 Apr 2018, 04:13
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B
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If |2x − 5| = 25 − x, what is the sum of the two possible values of x?

A. -20
B. -10
C. 10
D. 20
E. 30
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B
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If |2x − 5| = 25 − x, what is the sum of the two possible values of x? 10 Apr 2018, 04:24
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Bunuel
If |2x − 5| = 25 − x, what is the sum of the two possible values of x?

A. -20
B. -10
C. 10
D. 20
E. 30
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Case 1: 2x-5 is positive:

2x-5=25-x
x=10

case 2: 2x-5 is negative :

-(2x-5)=25-x
-2x + 5 = 25-x
x= -20

so, the sum of 2 possible values od x = 10 + (-20)
=-10

The correct answer is B.
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If |2x − 5| = 25 − x, what is the sum of the two possible values of x? 11 Apr 2018, 16:18
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Bunuel
If |2x − 5| = 25 − x, what is the sum of the two possible values of x?

A. -20
B. -10
C. 10
D. 20
E. 30
Show more


When (2x - 5) is positive, we have:

2x - 5 = 25 - x

3x = 30

x = 10

When (2x - 5) is negative we have:

-2x + 5 = 25 - x

-20 = x

So the sum is 10 + (-20) = -10.

Answer: B
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If |2x − 5| = 25 − x, what is the sum of the two possible values of x? Updated on: 11 Oct 2024, 12:14
Originally posted by BrushMyQuant on 28 May 2022, 03:34.
Last edited by BrushMyQuant on 11 Oct 2024, 12:14, edited 4 times in total.
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Given that |2x − 5| = 25 − x and we need to find the sum of the two possible values of x



To open |2x − 5| = 25 − x, we need to take two cases
(Watch this video to MASTER Absolute Value)
Case 1: Assume that whatever is inside the Absolute Value/Modulus is non-negative
=> 2x − 5 ≥ 0 => 2x ≥ 5 => x ≥ \(\frac{5}{2}\)

|2x − 5| = 2x − 5 (as if A ≥ 0 then |A| = A)
=> 2x − 5 = 25 − x
=> 2x + x = 25 + 5 = 30
=> 3x = 30
=> x = 10

And our condition was x ≥ \(\frac{5}{2}\). Definitely 10 ≥ \(\frac{5}{2}\)
=> x = 10 is a solution		Case 2: Assume that whatever is inside the Absolute Value/Modulus is Negative
2x − 5 < 0 => x < \(\frac{5}{2}\)

|2x − 5| = -(2x − 5) (as if A < 0 then |A| = -A)
=> -(2x − 5) = 25 − x
=> -2x + 5 = 25 - x
=> -2x +x = 25-5
=> -x = 20
=> x = -20
And our condition was x < \(\frac{5}{2}\). Definitely -20 < \(\frac{5}{2}\)
=> x = -20 is a solution

=> Sum of all the two possible values of x = 10 + (-20) = 10-20 = -10

So, Answer will be B
Hope it helps!

Watch the following video to MASTER Absolute Value Problems

­
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If |2x − 5| = 25 − x, what is the sum of the two possible values of x? 04 Jul 2024, 19:46
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­The answer is B.
Solve for 
1) 2x -5 = 25 -x : 10
2) -2x +5 = 25 -x : -20
Add the values you get and thats your answer : -20 +10 = -10
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