Question

Solve each of the following equation and also check your result in each case:
$\frac{5x}{3}-\frac{(x-1)}{4}=\frac{(x-3)}{5}$

Answer 1

$$\begin{gathered} \frac{5\mathrm{x}}{3}-\frac{\mathrm{x}-1}{4}=\frac{\mathrm{x}-3}{5} \\ \mathrm{or}\frac{20\mathrm{x}-3\mathrm{x}+3}{12}=\frac{\mathrm{x}-3}{5} \\ \mathrm{or}\frac{17\mathrm{x}+3}{12}=\frac{\mathrm{x}-3}{5} \\ \mathrm{or}85\mathrm{x}+15=12\mathrm{x}-36 \\ \mathrm{or}73\mathrm{x}=-51 \\ \mathrm{or}\mathrm{x}=\frac{-51}{73} \\ \mathrm{Check}: \\ \mathrm{L}.\mathrm{H}.\mathrm{S}.=\frac{5\times \frac{-51}{73}}{3}-\frac{\frac{-51}{73}-1}{4}=\frac{-255}{219}-\frac{-124}{292}=\frac{-54}{73} \\ \mathrm{R}.\mathrm{H}.\mathrm{S}.=\frac{\frac{-51}{73}-3}{5}=\frac{-54}{73} \end{gathered}$$

$\therefore$ L.H.S. = R.H.S. for x = $\frac{-51}{73}$