Question:
$\frac{2 x-1}{5}=\frac{3 x+1}{3}$
Solution:
Given $\frac{2 x-1}{5}=\frac{3 x+1}{3}$
$\Rightarrow$ $3(2 x-1)=5(3 x+1)$ [by cross-multiplication]
$\Rightarrow$ $6 x-3=15 x+5$
$\Rightarrow$ $6 x-15 x=3+5$ [transposing $15 x$ to LHS and $-3$ to RHS]
$\Rightarrow$ $-9 x=8$
$\Rightarrow$ $\frac{-9 x}{-9}=\frac{8}{-9}$ [dividing both sides by $-9$ ]
$\therefore$$x=\frac{-8}{9}$
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