Chapter 4 - Proportions, Percents, and Solving Inequalities - 4.5 - Inequalities, Compound Inequalities, and Problem Solving - Problem Set 4.5 - Page 175: 28

$x\gt-4$

Using the Distributive Property and the properties of inequalities, the solution to the given inequality, $ 2(x+1)+3(x+2)\gt-12 ,$ is \begin{array}{l}\require{cancel} 2x+2+3x+6\gt-12 \\\\ 2x+3x\gt-12-2-6 \\\\ 5x\gt-20 \\\\ x\gt-\dfrac{20}{5} \\\\ x\gt-4 .\end{array}