Question

Solve the following equation and verify your answer:

xix). $\frac{15(2-x)-5(x+6)}{1-3x}=10$

Answer 1

Given: $\frac{15(2-x)-5(x+6)}{1-3x}=10$

$\Rightarrow \frac{(30-15x)-(5x+30)}{(1-3x)}=10$

$\Rightarrow (30-15x)–(5x+30)=10(1-3x)$

$\Rightarrow 30-15x–5x–30=10–30x$

$\Rightarrow -15x–5x+30x=10$

$\Rightarrow 10x=10$

$\Rightarrow x=\frac{10}{10}$

$\Rightarrow x=1$

To check: $\frac{15(2-x)-5(x+6)}{1-3x}=10$ for $x=1$

$L.H.S=\frac{15(2-x)-5(x+6)}{1-3x}$

$=\frac{\left(15\right(2-1)–5(1+6\left)\right)}{(1-3)}$

$=\frac{15–5\left(7\right)}{-2}$

$=\frac{15-35}{-2}$

$=\frac{-20}{-2}$

$=10=R.H.S$

$\therefore L.H.S=R.H.S$

Hence, the given equation is verified for $x=1$.