a) $|x-3|=7-(-2)$
$⇔|x-3|=9$
$⇔ \left[ \begin{array}{l}x-3=9\\x-3=-9\end{array} \right.$
$⇔ \left[ \begin{array}{l}x=12\\x=-6\end{array} \right.$
b) $9x-1=81$
$⇔9x=82$
$⇔x=\frac{82}{9}$
c) $(x+1)+(x+2)+...+(x+100)=5750$
$⇔100x+ \frac{100.101}{2}=5750$
$⇔100x=700$
$⇔x=7$