Question

Solve:$\frac{x+35}{6}-\frac{x+7}{9}=\frac{x+21}{4}$

Answer 1

$\frac{x+35}{6}-\frac{x+7}{9}=\frac{x+21}{4}$

Factors of $6=2\times 3$

Factors of $9=3\times 3$

L.C.M of $6,9=18$

$\Rightarrow \frac{3(x+35)}{18}-\frac{2(x+7)}{18}=\frac{x+21}{4}$

$\Rightarrow \frac{3x+105}{18}-\frac{2x+14}{18}=\frac{x+21}{4}$

$\Rightarrow \frac{3x+105-2x-14}{18}=\frac{x+21}{4}$

$\Rightarrow \frac{x+91}{18}=\frac{x+21}{4}$

$\Rightarrow \frac{x+91}{9}=\frac{x+21}{2}$

$\Rightarrow 2x+182=9x+189$

$\Rightarrow 9x-2x=182-189=-7$

$\Rightarrow 7x=-7$

$\Rightarrow x=\frac{-7}{7}=-1$

$\therefore x=-1$