#### Answer

$x=10$

#### Work Step by Step

Using cross-multiplication and 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
\\\\
x=10
.\end{array}