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

The solution to x/((x+1))< 2/((3x-1)) is -1<x<(3-sqrt(33))/6 \lor 1/3 <x<(3+sqrt(33))/6

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

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

- 1 < x < \frac{3 - 33}{6} or \frac{1}{3} < x < \frac{3 + 33}{6}

Interval Notation

(- 1, \frac{3 - 33}{6}) \cup (\frac{1}{3}, \frac{3 + 33}{6})

Decimal Notation

- 1 < x < - 0.45742 \dots or 0.33333 \dots < x < 1.45742 \dots

Solution steps

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

Rewrite in standard form

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

Factor

3 x^{2} - 3 x - 2 : (x - \frac{3 + 33}{6}) (x - \frac{3 - 33}{6})

\frac{( x - \frac{3 + 33}{6} ) ( x - \frac{3 - 33}{6} )}{( x + 1 ) ( 3 x - 1 )} < 0

Identify the intervals

- 1 < x < \frac{3 - 33}{6} or \frac{1}{3} < x < \frac{3 + 33}{6}

- 4 x^{2} - x = 6

(2 x^{5}) (3 x + 2) < 0

- 7 x + 6 \geq - 3 x - 2

\frac{2}{x + 3} < \frac{1}{x + 1}

3 + 8 x = 5 x

What is x/((x+1))< 2/((3x-1)) ?
The solution to x/((x+1))< 2/((3x-1)) is -1<x<(3-sqrt(33))/6 \lor 1/3 <x<(3+sqrt(33))/6