What is (3x-5)/(4+1)> 1/(2x-1) ?

The solution to (3x-5)/(4+1)> 1/(2x-1) is 0 13/6

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(3x-5)/(4+1)> 1/(2x-1)

\frac{3 x - 5}{4 + 1} > \frac{1}{2 x - 1}

0 < x < \frac{1}{2} or x > \frac{13}{6}

Interval Notation

(0, \frac{1}{2}) \cup (\frac{13}{6}, \infty)

Decimal Notation

0 < x < 0.5 or x > 2.16666 \dots

Solution steps

\frac{3 x - 5}{4 + 1} > \frac{1}{2 x - 1}

Rewrite in standard form

\frac{6 x ^{2} - 13 x}{2 x - 1} > 0

Factor

\frac{6 x ^{2} - 13 x}{2 x - 1} : \frac{x ( 6 x - 13 )}{2 x - 1}

\frac{x ( 6 x - 13 )}{2 x - 1} > 0

Identify the intervals

0 < x < \frac{1}{2} or x > \frac{13}{6}

(4 x - 6)^{2} \geq (6 x - 4)^{2}

7 x^{9} - 4 > 17

x^{2} + x - 8 \geq x - x^{2} - 10

\frac{x + 1}{x ^{2} + 2} > \frac{1}{4}

\frac{( - x ^{2} + 4 x - 3 )}{( 2 x - 6 )} < 0

What is (3x-5)/(4+1)> 1/(2x-1) ?
The solution to (3x-5)/(4+1)> 1/(2x-1) is 0<x< 1/2 \lor x> 13/6