Question

Solve each of the following equation and also check your result in each case:
$\frac{7}{2}x-\frac{5}{2}x=\frac{20}{3}x+10$

Answer 1

$$\begin{gathered} \frac{7}{2}\mathrm{x}-\frac{5}{2}\mathrm{x}=\frac{20}{3}\mathrm{x}+10 \\ \mathrm{or}\frac{7\mathrm{x}-5\mathrm{x}}{2}=\frac{20\mathrm{x}+30}{3} \\ \mathrm{or}40\mathrm{x}+60=6\mathrm{x} \\ \mathrm{or}34\mathrm{x}=-60 \\ \mathrm{or}\mathrm{x}=-\frac{60}{34}=-\frac{30}{17} \\ \mathrm{Check}: \\ \mathrm{L}.\mathrm{H}.\mathrm{S}.=\frac{7}{2}\times \frac{-30}{17}-\frac{5}{2}\times -\frac{30}{17}=-\frac{30}{17} \\ \mathrm{R}.\mathrm{H}.\mathrm{S}.=\frac{20}{3}\times \frac{-30}{17}+10=-\frac{30}{17} \\ \therefore \mathrm{L}.\mathrm{H}.\mathrm{S}.=\mathrm{R}.\mathrm{H}.\mathrm{S}.\mathrm{for}\mathrm{x}=-\frac{30}{17} \end{gathered}$$