Question

Solve the following equation and verify your answer:

$\left(i\right)$ $\frac{2x-3}{3x+2}=-\frac{2}{3}$

Answer 1

Given: $\frac{(2x-3)}{(3x+2)}=-\frac{2}{3}$

$3(2x–3)=-2(3x+2)$

$6x–9=-6x–4$

$6x+6x=9–4$

$12x=5$

$x=\frac{5}{12}$

To check: $\frac{(2x-3)}{(3x+2)}=-\frac{2}{3}$ for $x=\frac{5}{12}$

$\text{L.H.S}=\frac{(2\left(\frac{5}{12}\right)–3)}{(3\left(\frac{5}{12}\right)+2)}$

$=\frac{(\left(\frac{5}{6}\right)-3)}{(\left(\frac{5}{4}\right)+2)}$

$=\frac{\left(\frac{5-18}{6}\right)}{\left(\frac{5+8}{4}\right)}$

$=\frac{(-\frac{13}{6})}{\left(\frac{13}{4}\right)}$

$=(-\frac{13}{6})\times \left(\frac{4}{13}\right)$

$=-\frac{4}{6}$

$=-\frac{2}{3}=\text{R.H.S}$

$\therefore \text{L.H.S = R.H.S}$

Hence, the given equation is verified for $x=\frac{5}{12}.$