Question

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

Answer 1

$2x-\frac{1}{2}=3$
⇒ 2x $-$$\frac{1}{2}$ + $\frac{1}{2}$ = 3 + $\frac{1}{2}$ [Adding $\frac{1}{2}$ on both the sides]
⇒ 2x = $\frac{6+1}{2}$
⇒ 2x = $\frac{7}{2}$
⇒ $\frac{2x}{2}=\frac{7}{2\times 2}$ [Dividing both the sides by 3]
⇒ x = $\frac{7}{4}$
Verification:
Substituting x = $\frac{7}{4}$ in the L.H.S.:
$$\begin{gathered} 2\left(\frac{7}{4}\right)-\frac{1}{2} \\ =\frac{7}{2}-\frac{1}{2}=\frac{6}{2}=3=R.H.S. \end{gathered}$$
L.H.S. = R.H.S.
Hence, verified.