Answer
$z=\dfrac{7}{6}$
Work Step by Step
Using the properties of equality, the solution to the given equation, $
2z-5+3z=4-(z+2)
$ is
\begin{array}{l}\require{cancel}
2z-5+3z=4-z-2
\\\\
2z+3z+z=4-2+5
\\\\
6z=7
\\\\
z=\dfrac{7}{6}
.\end{array}