Solve the following equation : 2 x-13 5 -x-3 11 =x-9 5 +1 - Vidyadip

Question

Solve the following equation : $\frac{2 x-13}{5}-\frac{x-3}{11}=\frac{x-9}{5}+1$

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Answer

$\frac{2 x-13}{5}-\frac{x-3}{11}=\frac{x-9}{5}+\frac{1}{1}$
Since, $\text{L.C.M}$. of denominators $5, 11, 5 $ and $1=55$
$\therefore \frac{2 x-13}{5} \times 55-\frac{x-3}{11} \times 55=\frac{x-9}{5} \times 55+\frac{1}{1} \times 55$
$ \Rightarrow 11(2 x-13)-5(x-3)=11(x-9)+55$
$ \Rightarrow 22 x-143-5 x+15=11 x-99+55$
$ \Rightarrow 22 x-5 x-11 x=-99+55+143-15$
$ \Rightarrow 6 x=198-114$
$ \Rightarrow 6 x=84$
$ \Rightarrow x=\frac{84}{6}$
$ \Rightarrow x=14$

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