#### Answer

$x\gt-\dfrac{5}{32}$

#### Work Step by Step

Using the Distributive Property and the properties of inequality, the solution to the given inequality, $
\dfrac{2}{3}\left(\dfrac{7}{8}-4x\right)-\dfrac{5}{8}\lt\dfrac{3}{8}
,$ is
\begin{array}{l}\require{cancel}
\dfrac{2}{3}\left(\dfrac{7}{8}\right)+\dfrac{2}{3}(-4x)-\dfrac{5}{8}\lt\dfrac{3}{8}
\\\\
\dfrac{14}{24}-\dfrac{8}{3}x-\dfrac{5}{8}\lt\dfrac{3}{8}
\\\\
24\left( \dfrac{14}{24}-\dfrac{8}{3}x-\dfrac{5}{8}\right)\lt\left(\dfrac{3}{8}\right)24
\\\\
1(14)+8(-8x)+3(-5)\lt3(3)
\\\\
14-64x-15\lt9
\\\\
-64x\lt9-14+15
\\\\
-64x\lt10
\\\\
x\gt\dfrac{10}{-64}
\\\\
x\gt\dfrac{\cancel{2}\cdot5}{\cancel{2}\cdot(-32)}
\\\\
x\gt\dfrac{5}{-32}
\\\\
x\gt-\dfrac{5}{32}
.\end{array}