What is 4/x-3> 2/(3x-1) ?

The solution to 4/x-3> 2/(3x-1) is 0<x< 1/3 \lor 4/9 <x<1

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4/x-3> 2/(3x-1)

\frac{4}{x} - 3 > \frac{2}{3 x - 1}

0 < x < \frac{1}{3} or \frac{4}{9} < x < 1

Interval Notation

(0, \frac{1}{3}) \cup (\frac{4}{9}, 1)

Decimal Notation

0 < x < 0.33333 \dots or 0.44444 \dots < x < 1

Solution steps

\frac{4}{x} - 3 > \frac{2}{3 x - 1}

Rewrite in standard form

\frac{- 9 x ^{2} + 13 x - 4}{x ( 3 x - 1 )} > 0

Factor

\frac{- 9 x ^{2} + 13 x - 4}{x ( 3 x - 1 )} : \frac{- ( 9 x - 4 ) ( x - 1 )}{x ( 3 x - 1 )}

\frac{- ( 9 x - 4 ) ( x - 1 )}{x ( 3 x - 1 )} > 0

Multiply both sides by

- 1

(reverse the inequality)

\frac{( - ( 9 x - 4 ) ( x - 1 ) ) ( - 1 )}{x ( 3 x - 1 )} < 0 \cdot (- 1)

Simplify

\frac{( 9 x - 4 ) ( x - 1 )}{x ( 3 x - 1 )} < 0

Identify the intervals

0 < x < \frac{1}{3} or \frac{4}{9} < x < 1

- 3 \leq x < 0

4 x^{2} - 3 x + 5 = 0

1 0^{- 13}

m^{2} + 9 m + 20 = 0

x^{2} - 11 x y + 28 y^{2}

What is 4/x-3> 2/(3x-1) ?
The solution to 4/x-3> 2/(3x-1) is 0<x< 1/3 \lor 4/9 <x<1