Question
Solve the following equation and verify your answer:
$\frac{2\text{x}-3}{3\text{x}+2}=-\frac{2}{3}$
$\frac{2\text{x}-3}{3\text{x}+2}=-\frac{2}{3}$
✓
Answer
$\frac{2\text{x}-3}{3\text{x}+2}=-\frac{2}{3}$
$6\text{x}-9=-6\text{x}-4$ (After cross multiplication)
$6\text{x}+6\text{x}=-4+9$
$\text{x}=\frac{5}{12}$
$\therefore\text{x}=\frac{5}{12}$ is the solution of the given equation.
Chek:
$\text{L.H.S.}=\frac{2\times\frac{5}{12}-3}{3\times\frac{5}{12}+2}=\frac{\frac{5}{6}-3}{\frac{5}{4}+2}=\frac{-4}{6}=\frac{-2}{3}$
$\text{R.H.S.}=\frac{-2}{3}$
$\text{L.H.S.}=\text{R.H.S.} \text{ for} \text{ x}=\frac{5}{12}$
$6\text{x}-9=-6\text{x}-4$ (After cross multiplication)
$6\text{x}+6\text{x}=-4+9$
$\text{x}=\frac{5}{12}$
$\therefore\text{x}=\frac{5}{12}$ is the solution of the given equation.
Chek:
$\text{L.H.S.}=\frac{2\times\frac{5}{12}-3}{3\times\frac{5}{12}+2}=\frac{\frac{5}{6}-3}{\frac{5}{4}+2}=\frac{-4}{6}=\frac{-2}{3}$
$\text{R.H.S.}=\frac{-2}{3}$
$\text{L.H.S.}=\text{R.H.S.} \text{ for} \text{ x}=\frac{5}{12}$
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