Question:
$\frac{x+1}{4}=\frac{x-2}{3}$
Solution:
Given, $\frac{x+1}{4}=\frac{x-2}{3}$
$\Rightarrow \quad 3(x+1)=4(x-2)$ [by cross-multiplication]
$\Rightarrow \quad 3 x+3=4 x-8$
$\Rightarrow$ $3 x-4 x=-8-3$ [transposing $4 x$ to LHS and 3 to RHS]
$\Rightarrow$ $-x=-11$ [dividing both sides by $-1$ ]
$\Rightarrow$ $\frac{-x}{-1}=\frac{-11}{-1}$
$\therefore$ $x=11$