#### Answer

$x\lt6$

#### Work Step by Step

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}