Question

Solve for $x$ in the following equation:
$\frac{x+5}{6}-\frac{x+1}{9}=\frac{x+3}{4}$

Answer 1

$\frac{x+5}{6}-\frac{x+1}{9}=\frac{x+3}{4}$
$\Rightarrow \frac{9(x+5)-6(x+1)}{6\times 9}=\frac{x+3}{4}$
$\Rightarrow \frac{9x+45-6x-6}{54}=\frac{x+3}{4}$
$\Rightarrow \frac{3x+39}{54}=\frac{x+3}{4}$

$\Rightarrow 4(3x+39)=54(x+3)$
$\Rightarrow 12x+156=54x+162$
​​​​​​​$\Rightarrow 54x-12x=156-162$
​​​​​​​$\Rightarrow 42x=-6$
​​​​​​​$\Rightarrow x=-\frac{1}{7}$