What is x/(2x-1)>= 3/(x+2) ?

The solution to x/(2x-1)>= 3/(x+2) is x = 3

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x/(2x-1)>= 3/(x+2)

\frac{x}{2 x - 1} \geq \frac{3}{x + 2}

x < - 2 or \frac{1}{2} < x \leq 1 or x \geq 3

Solution steps

\frac{x}{2 x - 1} \geq \frac{3}{x + 2}

Rewrite in standard form

\frac{x ^{2} - 4 x + 3}{( x + 2 ) ( 2 x - 1 )} \geq 0

Factor

\frac{x ^{2} - 4 x + 3}{( x + 2 ) ( 2 x - 1 )} : \frac{( x - 1 ) ( x - 3 )}{( x + 2 ) ( 2 x - 1 )}

\frac{( x - 1 ) ( x - 3 )}{( x + 2 ) ( 2 x - 1 )} \geq 0

Identify the intervals

x < - 2 or \frac{1}{2} < x \leq 1 or x \geq 3

\frac{4 x ^{\frac{5}{4}} - 2 x ^{\frac{1}{4}}}{x ^{\frac{1}{4}}}

5 x^{2} - 3 x - 1 = 0

y^{2} = - 4

\frac{j}{4} = 3

4 p - 1 \leq 3 p - 10

What is x/(2x-1)>= 3/(x+2) ?
The solution to x/(2x-1)>= 3/(x+2) is x<-2\lor 1/2 <x<= 1\lor x>= 3