Question

Solve the following equations and verify your answer :
$\frac{15(2-x)-5(x+6)}{1-3x}=10$

Answer 1

Given $\frac{15(2-x)-5(x+6)}{1-3x}=\frac{10}{1}$
$\Rightarrow \frac{30-15x-5x-30}{1-3x}=\frac{10}{1}$
$\Rightarrow \frac{-20x}{1-3x}=\frac{10}{1}$
By cross multiplication :
$-20x=10(1-3x)$
$\Rightarrow -20x=10-30x$
$\Rightarrow -20x+30x=10\Rightarrow 10x=10$
$\Rightarrow x=\frac{10}{10}=1$
$\therefore x=1$
Verification :
Consider, L.H.S. $=\frac{15(2-x)-5(x+5)}{1-3x}$
$=\frac{15(2-1)-5(1+6)}{1-3\times 1}$
$=\frac{(15\times 1)-(5\times 7)}{1-3}=\frac{15-35}{-2}$
$=\frac{-20}{-2}=10$
$=$R.H.S
Hence, verified.