Question

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

Answer 1

$$\begin{gathered} \mathrm{x}-\frac{\mathrm{x}-1}{2}=1-\frac{\mathrm{x}-2}{3} \\ \mathrm{or}\frac{2\mathrm{x}-\mathrm{x}+1}{2}=\frac{3-\mathrm{x}+2}{3} \\ \mathrm{or}\frac{\mathrm{x}+1}{2}=\frac{5-\mathrm{x}}{3} \\ \mathrm{or}3\mathrm{x}+3=10-2\mathrm{x} \\ \mathrm{or}5\mathrm{x}=10-3 \\ \mathrm{or}\mathrm{x}=\frac{7}{5} \\ \mathrm{Check}: \\ \mathrm{L}.\mathrm{H}.\mathrm{S}.=\frac{7}{5}-\frac{\frac{7}{5}-1}{2}=\frac{7}{5}-\frac{1}{5}=\frac{6}{5} \\ \mathrm{R}.\mathrm{H}.\mathrm{S}.=1-\frac{\frac{7}{5}-2}{3}=1-\frac{-3}{15}=\frac{6}{5} \end{gathered}$$

$\therefore$ L.H.S. = R.H.S. for x = $\frac{7}{5}$