Question

Solve each of the following equation and also check your result in each case:
$\frac{3x}{4}-\frac{(x-1)}{2}=\frac{(x-2)}{3}$

Answer 1

$$\begin{gathered} \frac{3\mathrm{x}}{4}-\frac{\mathrm{x}-1}{2}=\frac{\mathrm{x}-2}{3} \\ \mathrm{or}\frac{3\mathrm{x}-2\mathrm{x}+2}{4}=\frac{\mathrm{x}-2}{3} \\ \mathrm{or}4\mathrm{x}-8=3\mathrm{x}+6 \\ \mathrm{or}\mathrm{x}=14 \\ \mathrm{Check}: \\ \mathrm{L}.\mathrm{H}.\mathrm{S}.=\frac{3\times 14}{4}-\frac{14-1}{2}=\frac{21}{2}-\frac{13}{2}=\frac{8}{2}=4 \\ \mathrm{R}.\mathrm{H}.\mathrm{S}.=\frac{14-2}{3}=\frac{12}{3}=4 \end{gathered}$$

$\therefore$ L.H.S. = R.H.S. for x = 14