Question

Solve each of the following equation and also verify your solution:
$\frac{2x-1}{3}-\frac{6x-2}{5}=\frac{1}{3}$

Answer 1

$$\begin{gathered} \frac{2\mathrm{x}-1}{3}-\frac{6\mathrm{x}-2}{5}=\frac{1}{3} \\ \mathrm{or}\frac{10\mathrm{x}-5-18\mathrm{x}+6}{15}=\frac{1}{3} \\ \mathrm{or}\frac{-8\mathrm{x}+1}{15}=\frac{1}{3} \\ \mathrm{or}-24\mathrm{x}+3=15 \\ \mathrm{or}24\mathrm{x}=3-15 \\ \mathrm{or}\mathrm{x}=\frac{-12}{24}=\frac{-1}{2} \\ \mathrm{Verification}: \\ \mathrm{L}.\mathrm{H}.\mathrm{S}.=\frac{2\times {\displaystyle \frac{-1}{2}}-1}{3}-\frac{6\times {\displaystyle \frac{-1}{2}}-2}{5} \\ =\frac{-2}{3}-\frac{-5}{5} \\ =\frac{-2+3}{3}=\frac{1}{3}=\mathrm{R}.\mathrm{H}.\mathrm{S}. \end{gathered}$$