Equivalent to an absolute value

[Dances]

I can see the correct answer, but how do you mathematically arrive to it?:

If /x-10/=b, where x<10, then which of the following is equivalent to b-x?
A) -10
B) 10
C) 2b-10
D) 10-2b

The "/" is supposed to be absolute value. I know the answer is C, but how do I explain that?

 

[skeeter]

[MATH]|x-10| = b[/MATH]
[MATH]x < 10 \implies 10-x = b \implies x = 10-b \implies b-x = b-(10-b) = 2b-10[/MATH]

 

[Dances]

Skeeter...brilliant work! Thank you.

 

[Steven G]

Skeeter is brilliant but in this problem Skeeter used the definition of absolute values. BTW, look at the key above the enter button.

 

[Dances]

|Thanks|