Question

Solve each of the following equation and also check your result in each case:
$\frac{1}{2}x+7x-6=7x+\frac{1}{4}$

Answer 1

$$\begin{gathered} \frac{1}{2}\mathrm{x}+7\mathrm{x}-6=7\mathrm{x}+\frac{1}{4} \\ \mathrm{or}\frac{1}{2}\mathrm{x}+7\mathrm{x}-7\mathrm{x}=\frac{1}{4}+6 \\ \text{or}\frac{x}{2}=\frac{1+24}{4} \\ \mathrm{or}\frac{\mathrm{x}}{2}=\frac{25}{4} \\ \mathrm{or}\mathrm{x}=\frac{25}{2} \\ \mathrm{Check}: \\ \mathrm{L}.\mathrm{H}.\mathrm{S}.=\frac{1}{2}\times \frac{25}{2}+7\times \frac{25}{2}-6=\frac{351}{4} \\ \mathrm{R}.\mathrm{H}.\mathrm{S}.=7\times \frac{25}{2}+\frac{1}{4}=\frac{351}{4} \end{gathered}$$

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