Question

Solve the following equation and verify your answer:

xvi). $\frac{9x-7}{3x+5}=\frac{3x-4}{x+6}$

Answer 1

Given: $\frac{9x-7}{3x+5}=\frac{3x-4}{x+6}$

$\Rightarrow \frac{9x-7}{3x+5}-\frac{3x-4}{x+6}=0$

$\Rightarrow \frac{(9x-7)(x+6)–(3x-4)(3x+5)}{(3x+5)(x+6)}=0$

$\Rightarrow (9x-7)(x+6)–(3x-4)(3x+5)=0$

$\Rightarrow 9x^2+54x–7x–42–(9x^2+15x–12x–20)=0$

$\Rightarrow 44x–22=0$

$\Rightarrow 44x=22$

$\Rightarrow x=\frac{1}{2}$

To check: $\frac{9x-7}{3x+5}=\frac{3x-4}{x+6}$ for $x=\frac{1}{2}$

$L.H.S=\frac{9x-7}{3x+5}$

$=\frac{9\left(\frac{1}{2}\right)-7}{3\left(\frac{1}{2}\right)+5}$

$=\frac{\frac{9}{2}-7}{\frac{3}{2}+5}$

$=\frac{\frac{9-14}{2}}{\frac{3+10}{2}}=\frac{-\frac{5}{2}}{\frac{13}{2}}=-\frac{5}{13}$

$R.H.S=\frac{3x-4}{x+6}$

$=\frac{3\left(\frac{1}{2}\right)-4}{\left(\frac{1}{2}\right)+6}$

$=\frac{\frac{3}{2}-4}{\frac{1}{2}+6}$

$=\frac{\frac{3-8}{2}}{\frac{1+12}{2}}$

$=\frac{-\frac{5}{2}}{\frac{13}{2}}$

$=-\frac{5}{13}$

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

Hence, the given equation is verified for $x=\frac{1}{2}$.