prove that

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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