Question

Question 1
Solve the linear equation $\frac{x}{2}-\frac{1}{5}=\frac{x}{3}+\frac{1}{4}$

Answer 1

$\frac{x}{2}-\frac{1}{5}=\frac{x}{3}+\frac{1}{4}$
$\Rightarrow \frac{x}{2}-\frac{x}{3}=\frac{1}{4}+\frac{1}{5}\Rightarrow \frac{3x-2x}{6}=\frac{5+4}{20}$
$\Rightarrow \frac{x}{6}=\frac{9}{20}\Rightarrow x=\frac{9\times 6}{20}=\frac{27}{10}$
To check:
$\frac{x}{2}-\frac{1}{5}=\frac{x}{3}+\frac{1}{4}\Rightarrow \frac{27}{10\times 2}-\frac{1}{5}=\frac{27}{10\times 3}+\frac{1}{4}$
$\Rightarrow \frac{27}{20}-\frac{1}{5}=\frac{9}{10}+\frac{1}{4}$ $\Rightarrow \frac{27-4}{20}=\frac{18+5}{20}$
$\Rightarrow \frac{23}{20}=\frac{23}{20}$
$\Rightarrow L.H.S=R.H.S$
Therefore, it is correct.