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

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

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

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

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

Interval Notation

(- 2, \frac{1}{2}) \cup [1, 3]

Decimal Notation

- 2 < x < 0.5 or 1 \leq x \leq 3

Solution steps

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

Rewrite in standard form

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

Identify the intervals

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

∣ x - 5 ∣ = 7

4 (\frac{1}{4})

\frac{3 ( x - 7 )}{4} - x = 1 - \frac{x}{6}

3 x^{2} - x - 8 = 0

- 8 x = 20

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