#### Answer

$x\lt-\dfrac{9}{16}$

#### Work Step by Step

Multiplying both sides by the $LCD=
24
$ and then using the properties of inequalities, the solution to the given inequality, $
\dfrac{5x}{4}+\dfrac{3}{8}\lt\dfrac{7x}{12}
,$ is
\begin{array}{l}\require{cancel}
6(5x)+3(3)\lt2(7x)
\\\\
30x+9\lt14x
\\\\\
30x-14x+9 \lt 0
\\\\
30x-14x\lt-9
\\\\
16x\lt-9
\\\\
x\lt-\dfrac{9}{16}
.\end{array}