Question

Solve each of the following equations and also verify your solution :

$\frac{7}{2}x-\frac{5}{2}x=\frac{20}{3}x+10$

Answer 1

$\frac{7}{2}x-\frac{5}{2}x=\frac{20}{3}x+10\Rightarrow \frac{7}{2}x-\frac{5}{2}x-\frac{20}{3}x=10\frac{21x-15x-40x}{6}=10\Rightarrow =\frac{21x-55x}{6}=10\Rightarrow -\frac{34}{6}x=10-34x=10\times 6\Rightarrow x=\frac{10\times 6}{-34}=\frac{-30}{17}\therefore x=\frac{-30}{17}$
Verification:
$L.H.S.=\frac{7}{2}x-\frac{5}{2}x=\frac{7}{2}\times \frac{-30}{17}-\frac{5}{2}\times \frac{-30}{17}=\frac{-105}{17}+\frac{75}{17}=\frac{-105+75}{17}=\frac{-30}{17}R.H.S.=\frac{20}{3}x+10=\frac{20}{3}\times \frac{-30}{17}+10=\frac{-200}{17}+10=\frac{-200+170}{17}=\frac{-30}{17}\therefore L.H.S.=R.H.S.$