Question

Need to solve graphically by first converting to an equivalent equation with 0 on the right-hand side and then find the x-intercepts.
|2x-5|=4-|x-3|
HELP!?

Answer 1

There are 4 casses

Answer 2

\[\begin{split}
-(2x-5)&=4-(x-3)&\quad&2x-5<0&\quad&x-3>0\\
-(2x-5)&=4+(x-3)&&2x-5<0&&x-3<0\\
2x-5&=4-(x-3)&&2x-5>0&&x-3>0\\
2x-5&=4+(x-3)&&2x-5>0&&x-3<0
\end{split}
\]So there are \(4\) possible solutions. You have to find them all.

Answer 3

Some of these cases might actually be impossible though.