Solve each of the following equation and also check your result in each case:

$\frac{1}{2} x+7 x-6=7 x+\frac{1}{4}$

or $\frac{1}{2} \mathrm{x}+7 \mathrm{x}-7 \mathrm{x}=\frac{1}{4}+6$

or $\frac{x}{2}=\frac{1+24}{4}$

or $\frac{\mathrm{x}}{2}=\frac{25}{4}$

or $\mathrm{x}=\frac{25}{2}$

Check :

L.H.S. $=\frac{1}{2} \times \frac{25}{2}+7 \times \frac{25}{2}-6=\frac{351}{4}$

R.H.S. $=7 \times \frac{25}{2}+\frac{1}{4}=\frac{351}{4}$

$\therefore$ L.H.S. = R.H.S. for $x=\frac{25}{2}$