Solve each of the following equations and also verify your solution:
$$\dfrac {2x - 1}{3} - \dfrac {6x - 2}{5} = \dfrac {1}{3}$$.
$$\dfrac{2x - 1}{3} - \dfrac{6x - 2}{5} = \dfrac{1}{3}$$$$\dfrac{5(2x - 1) - 3 (6x -2)}{15} = \dfrac{1}{3}$$
$$5(2x - 1) - 3 (6x - 2) = 5$$
$$10x - 5 - 18x + 6 = 5$$
$$10x - 18x = 5 + 5 - 6$$
$$-8x = +4$$
$$x = \dfrac{-4}{8}$$
$$x = \dfrac{-1}{2}$$
Verification :-
$$LHS = \dfrac{2x - 1}{3} - \dfrac{6x - 2}{5}$$
$$= \dfrac{5 (2x - 1) - 3(6x - 2)}{15}$$
$$= \dfrac{10x - 5 - 18x + 6}{15}$$
$$= \dfrac{-8x + 1}{15} \Rightarrow \dfrac{-8 (-1/2) + 1}{15}$$
$$= \dfrac{4 + 1}{15} = \dfrac{5}{15}$$
$$= \dfrac{1}{3} = RHS$$