Chapter 4 - Proportions, Percents, and Solving Inequalities - 4.5 - Inequalities, Compound Inequalities, and Problem Solving - Problem Set 4.5 - Page 175: 27

$x\lt6$

Using the Distributive Property and the properties of inequalities, the solution to the given inequality, $ 3(x-4)+2(x+3)\lt24 ,$ is \begin{array}{l}\require{cancel} 3x-12+2x+6\lt24 \\\\ 3x+2x\lt24+12-6 \\\\ 5x\lt30 \\\\ x\lt\dfrac{30}{5} \\\\ x\lt6 .\end{array}