Chapter 4 - Proportions, Percents, and Solving Inequalities - 4.5 - Inequalities, Compound Inequalities, and Problem Solving - Problem Set 4.5 - Page 175: 36

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

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}