Question

Rewrite the expression in a form that does not contain absolute values.
|x-2| + |x-3|, if 2 < x < 3

Answer 1

since x>2, |x-2| >0 so |x-2|=(x-2)
since x<3, |x-3| <0 so |x-3|=-(x-3)
so what is
(x-2)-(x-3) = ?

Answer 2

if x is between 2 and 3
the \[\left| x-2 \right|\] will open with a positive sign
and the \[\left| x-3 \right|\] will open with a negative sign
hence
\[\left\{(+1)\left( x-2 \right) + (-1)(x-3) \right\}\]
hence the final answer will be
\[\left\{ x-2 -x+3 \right\} \]

Answer 3

you can simplify further ;)

Answer 4

isnt the answer1

Answer 5

Expression is x-2-x+3
its simplification = 1

Answer 6

@hartnn doesnt the expression also become 1, it's constant with no terms involving x, x-2-x+3 would mean nothing as a expression

Answer 7

I think the analysis done at the top are all good. Bravo to all . . .