Chapter 4 - Proportions, Percents, and Solving Inequalities - 4.5 - Inequalities, Compound Inequalities, and Problem Solving - Problem Set 4.5 - Page 175: 23

$x\lt8$

Using the Distributive Property and the properties of inequalities, the solution to the given inequality, $ 3(x-2)\lt2(x+1) ,$ is \begin{array}{l}\require{cancel} 3x-6\lt2x+2 \\\\ 3x-2x\lt2+6 \\\\ x\lt8 .\end{array}