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

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

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

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

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

Interval Notation

(- \infty, - 1) \cup (\frac{1}{3}, 3)

Decimal Notation

x < - 1 or 0.33333 \dots < x < 3

Solution steps

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

Rewrite in standard form

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

Identify the intervals

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

(2 x^{2} - 13 x - 27) (x^{2} - 2 x + 6) \leq 0

x^{2} - 3 x + 4 > - 2

\frac{- 1}{2 x} > 6

\frac{( x ^{3} + x ^{2} + x )}{( 9 x ^{2} - 25 )} \geq 0

(5 - x) \cdot (2 x - 6) > 0

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