Question

Solve each of the following equations and also check uour results in each case:

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

Answer 1

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

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

$\frac{21x-15x-40x}{6}=10$

$-\frac{34x}{6}=10$

$-34x=60$

$x=\frac{60}{-34}$

$x=-\frac{30}{17}$

To check: $\frac{7x}{2}-\frac{5x}{2}=\frac{20x}{3}+10forx=-\frac{30}{17}$

$L.H.S.=\frac{7x}{2}-\frac{5x}{2}$

$=\left(\frac{7}{2}\right)(-\frac{30}{17})-\left(\frac{5}{2}\right)(-\frac{30}{17})$

$=-\frac{210}{34}+\frac{150}{34}$

$=-\frac{30}{17}$

$R.H.S.=\frac{20x}{3}+10$

$=\left(\frac{20}{3}\right)(-\frac{30}{17})+10$

$=-\frac{600}{51}+10$

$=\frac{-600+510}{51}$

$=-\frac{90}{51}$

$=-\frac{30}{17}$

Hence, the given equation is verified for $x=-\frac{30}{17}$.