# Math Help - Simplify absolute value

1. ## Simplify absolute value

My calculus assignment is asking this:

If 4x, simplify the expression by removing the absolute sign.
abs(4 - x) = ?

It is asking for only a single definite answer. What could this be? I really don't understand.

2. Using the definition of the absolute value

$|4-x|=4-x \ \ \ \mbox{if} \ \ 4-x>0$

$|4-x|=-(4-x) \ \ \mbox{if} \ \ 4-x<0$

Since $4

$\Rightarrow |4-x|=-(4-x)=x-4$

3. Slightly more succinctly, if 4< x, then 0< x- 4, 0> 4- x.