Answer
$x=10$
Work Step by Step
Multiplying both sides by the $LCD=
-12
$ and using the properties of equality, the value of the variable that satisfies the given equation, $
\dfrac{x-1}{-3}=\dfrac{x+2}{-4}
,$ is
\begin{array}{l}\require{cancel}
4(x-1)=3(x+2)
\\\\
4x-4=3x+6
\\\\
4x-3x=6+4
\\\\
x=10
.\end{array}
