Solve the following equation : x 3 -2 1 2 = 4 x 9 - 2 x 3 - Vidyadip

Question

Solve the following equation : $\frac{\mathrm{x}}{3}-2 \frac{1}{2}=\frac{4 \mathrm{x}}{9}-\frac{2 \mathrm{x}}{3}$

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Answer

$\Rightarrow \frac{x}{3}-\frac{5}{2}=\frac{4 x}{9}-\frac{2 x}{3}$
Since, $\text{L.C.M}$. of denominators $3, 2, 9$ and $3=18$
$\Rightarrow \frac{\mathrm{x}}{3} \times 18-\frac{5}{2} \times 18=\frac{4 \mathrm{x}}{9} \times 18-\frac{2 \mathrm{x}}{3} \times 18$
$.....[$Multiplying each term by $18]$
$\Rightarrow 6 x-45=8 x-12 x$
$\Rightarrow 6 x+12 x-8 x=45$
$\Rightarrow 18 x-8 x=45$
$\Rightarrow 10 \mathrm{x}=45$
$\Rightarrow x=\frac{45}{10}$
$\Rightarrow x=4.5$

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