Elementary Algebra

$x=10$
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}