Question

Solve each of the following equations and verify the answer in each case:
$\frac{2x}{5}-\frac{3}{2}=\frac{x}{2}+1$

Answer 1

$\frac{2x}{5}-\frac{3}{2}=\frac{x}{2}+1$
or, $\frac{2x}{5}-\frac{x}{2}=1+\frac{3}{2}$ [Transposing x/2 to the L.H.S. and 3/2 to R.H.S.]
$$\begin{gathered} or,\frac{4x-5x}{10}=\frac{2+3}{2} \\ or,\frac{-x}{10}=\frac{5}{2} \end{gathered}$$
$or,\frac{-x}{10}(-10)=\frac{5}{2}\times (-10)$ [Multiplying both the sides by −10]
or, x = −25
Verification:
Substituting x = −25 on both the sides:
$$\begin{gathered} L.H.S.:\frac{2(-25)}{5}-\frac{3}{2} \\ =\frac{-50}{5}-\frac{3}{2} \\ =-10-\frac{3}{2}=\frac{-23}{2} \\ R.H.S.:\frac{-25}{2}+1=\frac{-25+2}{2}=\frac{-23}{2} \end{gathered}$$
L.H.S. = R.H.S.
Hence, verified.