Question

Solve each of the following equations and verify the answer in each case:
$\frac{x-3}{5}-2=\frac{2x}{5}$

Answer 1

$\frac{x-3}{5}-2=\frac{2x}{5}$
or, $\frac{x}{5}-\frac{3}{5}-2=\frac{2x}{5}$
or, $-\frac{3}{5}-2=\frac{2x}{5}-\frac{x}{5}$ [Transposing x/5 to the R.H.S.]
or, $\frac{-3-10}{5}=\frac{x}{5}$
or, $\frac{-13}{5}=\frac{x}{5}$
or, $\frac{-13}{5}\left(5\right)=\frac{x}{5}\times \left(5\right)$ [Multiplying both the sides by 5]
or, x = −13
Verification:
Substituting x = −13 on both the sides:
$$\begin{gathered} L.H.S.:\frac{-13-3}{5}-2 \\ =\frac{-16}{5}-2=\frac{-16-10}{5}=\frac{-26}{5}R.H.S.:\frac{2\times (-13)}{5}\mathbf{}\mathbf{=}\mathbf{}\frac{-26}{5} \end{gathered}$$

L.H.S. = R.H.S.
Hence, verified.