Chapter 4 - Proportions, Percents, and Solving Inequalities - 4.5 - Inequalities, Compound Inequalities, and Problem Solving - Problem Set 4.5 - Page 175: 22

$x\gt\dfrac{29}{3}$

Using the properties of inequalities, the solution to the given inequality, $ -3(x-5)\lt-14 ,$ is \begin{array}{l}\require{cancel} (x-5)\gt\dfrac{-14}{-3} \\\\ x-5\gt\dfrac{14}{3} \\\\ x\gt\dfrac{14}{3}+5 \\\\ x\gt\dfrac{14}{3}+\dfrac{15}{3} \\\\ x\gt\dfrac{29}{3} .\end{array}