Chapter 3 - Equations and Problem Solving - 3.1 - Solving First-Degree Equations - Problem Set 3.1 - Page 100: 57

$x=\dfrac{27}{32}$

Multiplying both sides by the $LCD= 24 ,$ and using the properties of equality, the value of the variable that satisfies the given equation, $ -\dfrac{4}{3}x=-\dfrac{9}{8} ,$ is \begin{array}{l}\require{cancel} 8(-4x)=3(-9) \\\\ -32x=-27 \\\\ x=\dfrac{-27}{-32} \\\\ x=\dfrac{27}{32} .\end{array}