Rewrite the expression in a form without absolute values?

Question

I have no clue how to do this. Could someone please explain how to do this, and why (why did you have to do this step, etc)?

Rewrite the expression in a form w/o absolute values.

|x-3| + |x-4| where 3 < x < 4

The answer should come out to 1, but I don't know how/why it is.

Answer 1

The absolute value of a positive quantity is the same quantity. The absolute value of a negative quantity equals the quantity multiplied by -1.

x &gt; 3 so x - 3 &gt; 0 and |x - 3| = x - 3

x &lt; 4 so x - 4 &lt; 0 and |x - 4| = 4 - x

So if 3 &lt; x &lt; 4, |x - 3| + |x - 4| = (x - 3) + (4 - x)

= 4 - 3

= 1