Solve each of the following equation and also verify your solution:

$\frac{2 \mathrm{x}-1}{3}-\frac{6 \mathrm{x}-2}{5}=\frac{1}{3}$

or $\frac{10 \mathrm{x}-5-18 \mathrm{x}+6}{15}=\frac{1}{3}$

or $\frac{-8 \mathrm{x}+1}{15}=\frac{1}{3}$

or $-24 \mathrm{x}+3=15$

or $24 \mathrm{x}=3-15$

or $\mathrm{x}=\frac{-12}{24}=\frac{-1}{2}$

Verification :

L.H.S. $=\frac{2 \times \frac{-1}{2}-1}{3}-\frac{6 \times \frac{-1}{2}-2}{5}$

$=\frac{-2}{3}-\frac{-5}{5}$

$=\frac{-2+3}{3}=\frac{1}{3}=$ R. H.S.