Question

solve:-$\frac{2x - 1}{3} + 1 = \frac{x - 2}{3} + 2$And Check the result.​

Answer 1

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$\: \frac{2x - 1}{3} + 1 = \frac{x - 2}{3} + 2$

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

Thus,x=2 is the solution of the given equation.

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Answer 2

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$\: \frac{2x - 1}{3} + 1 = \frac{x - 2}{3} + 2$

$\begin{gathered}⇒ \frac{2x}{3} - \frac{1}{3} + 1 = \frac{x}{3} - \frac{2}{3} + 2 \\ ⇒ \frac{2x}{3} + \frac{3 - 1}{3} = \frac{x}{3} + \frac{6 - 2}{3} \\ ⇒ \frac{2x}{3} + \frac{2}{3} = \frac{x}{3} + \frac{4}{3} \\ ⇒ \frac{2x}{3} - \frac{x}{3} = \frac{4}{3} - \frac{2}{3} \\ ⇒ \frac{x}{3} = \frac{2}{3} \\ ⇒ \frac{x}{3} \times 3 = \frac{2}{3} \times 3 \\ ⇒ x = 2\end{gathered}$

Thus,x=2 is the solution of the given equation.