prove that

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 $-1$ ]

$\Rightarrow$ $\frac{-x}{-1}=\frac{-11}{-1}$

$\therefore$ $x=11$

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