x−23−2>0⇒x−23−2x+4>0⇒x−27−2x>0⇒(7−2x0 and x−2>0)⇒(72x and x>2)(x>27 and x2)⇒22 cannot hold]

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Solve: {3}{x-2}> 2, x R

Question

Solve:
$\frac{3}{x - 2} > 2, x \in R$

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Text solutionVerified

\frac{3}{x - 2} - 2 > 0 \Rightarrow \frac{3 - 2 x + 4}{x - 2} > 0 \Rightarrow \frac{7 - 2 x}{x - 2} > 0

\Rightarrow (7 - 2 x < 0

and

x - 2 < 0)

(7 - 2 x > 0

and

x - 2 > 0)

\Rightarrow (7 < 2 x

and

x < 2)

(7 > 2 x

and

x > 2)

(x > \frac{7}{2}

and

x < 2)

(x < \frac{7}{2}

and

x > 2)

\Rightarrow 2 < x < \frac{7}{2} \Rightarrow x \in (2, \frac{7}{2})

[x < \frac{7}{2}

and

x > 2

cannot hold]

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