Chapter 4 - Proportions, Percents, and Solving Inequalities - 4.5 - Inequalities, Compound Inequalities, and Problem Solving - Problem Set 4.5 - Page 175: 25

$x\lt21$

Using the Distributive Property and the properties of inequalities, the solution to the given inequality, $ 4(x+3)\gt6(x-5) ,$ is \begin{array}{l}\require{cancel} 4x+12\gt6x-30 \\\\ 4x-6x\gt-30-12 \\\\ -2x\gt-42 \\\\ x\lt\dfrac{-42}{-2} \\\\ x\lt21 .\end{array}