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# If 5|5-x|=3, what is the sum of all the possible values of x ?

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Re: If 5|5-x|=3, what is the sum of all the possible values of x ? [#permalink]
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Given that 5|5-x|=3 and we need to find the sum of all the possible values of x

To open 5|5-x|=3 we need to take two cases (Watch this video to know about the Basics of Absolute Value)

Case 1: Assume that whatever is inside the Absolute Value/Modulus is non-negative

=> 5 - x ≥ 0 => x ≤ 5

|5 - x| = 5 - x (as if A ≥ 0 then |A| = A)
=> 5*(5-x) = 3
=> 5 - x = $$\frac{3}{5}$$
=> x = 5 - $$\frac{3}{5}$$ = $$\frac{25 - 3}{5}$$ = $$\frac{22}{5}$$ = 4.4
And our condition was x ≤ 5. Definitely 4.4 ≤ 5
=> x = 4.4 is a solution

Case 2: Assume that whatever is inside the Absolute Value/Modulus is Negative

5 - x < 0 => x > 5
|5 - x| = -(5 - x) (as if A < 0 then |A| = -A)
=> 5*-(5-x) = 3
=> -5 + x = $$\frac{3}{5}$$
=> x = 5 + $$\frac{3}{5}$$ = $$\frac{25 + 3}{5}$$ = $$\frac{28}{5}$$ = 5.6
And our condition was x > 5. Definitely 5.6 > 5
=> x = 5.6 is a solution

=> Sum of all possible values of x = 4.4 + 5.6 = 10

So, Answer will be D
Hope it helps!

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

Re: If 5|5-x|=3, what is the sum of all the possible values of x ? [#permalink]
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