Answer
$x=46/5$
Work Step by Step
$\frac{x+2}{7}=5-\frac{x+1}{3}$
$\frac{1}{7}x+\frac{2}{7}=5-\frac{1}{3}x-\frac{1}{3}$
$\frac{1}{7}x+\frac{1}{3}x=5-\frac{1}{3}-\frac{2}{7}$
$\frac{10}{21}x=\frac{92}{21}$
$10x=92$
$x=\frac{92}{10}=\frac{46}{5}$