Answer
$x=\dfrac{23}{7}$
Work Step by Step
Using the properties of equality, the solution to the given equation, $
\dfrac{2}{3}(x-2)-1=-\dfrac{1}{2}(x-3)
$, is
\begin{array}{l}
6\left[ \dfrac{2}{3}(x-2)-1 \right]=\left[ -\dfrac{1}{2}(x-3) \right]6
\\\\
4(x-2)-6(1)=-3(x-3)
\\\\
4x-8-6=-3x+9
\\\\
4x+3x=9+8+6
\\\\
7x=23
\\\\
x=\dfrac{23}{7}
.\end{array}
