Answer
Solution set = $\{9.2\}$
Work Step by Step
Multiply both sides with the LCD, $21$
$ 21 \left[\displaystyle \frac{x+1}{3}\right]=21 \left[ 5-\dfrac{x+2}{7} \right]\quad$ ... distribute and simplify
$ 7(x+1)=105-3(x+2)\quad$ ... distribute and simplify
$7x+7=105-3x-6$
$ 7x+7=99-3x \quad$ ... add $3x-7$ to both sides
$7x+3x=99-7$
$10x=92$
$x=9.2$
Solution set = $\{9.2\}$
