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

The solution to 3/(5x-1)>2-x is 1/5 (11+sqrt(21))/(10)

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

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

\frac{1}{5} < x < \frac{11 - 21}{10} or x > \frac{11 + 21}{10}

Interval Notation

(\frac{1}{5}, \frac{11 - 21}{10}) \cup (\frac{11 + 21}{10}, \infty)

Decimal Notation

0.2 < x < 0.64174 \dots or x > 1.55825 \dots

Solution steps

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

Rewrite in standard form

\frac{5 x ^{2} - 11 x + 5}{5 x - 1} > 0

Factor

5 x^{2} - 11 x + 5 : (x - \frac{11 + 21}{10}) (x - \frac{11 - 21}{10})

\frac{( x - \frac{11 + 21}{10} ) ( x - \frac{11 - 21}{10} )}{5 x - 1} > 0

Identify the intervals

\frac{1}{5} < x < \frac{11 - 21}{10} or x > \frac{11 + 21}{10}

24 x^{4} + 2 x^{3} - 5 x^{2} - x \geq 0

4 x^{3} - 9 x^{2} - 11 x + 26 \geq 0

x^{2} + x + 3 < 0

\frac{1}{( 4 x - 1 )} > 2

(x - 4) (x + 5) > 0

What is 3/(5x-1)>2-x ?
The solution to 3/(5x-1)>2-x is 1/5 <x<(11-sqrt(21))/(10)\lor x>(11+sqrt(21))/(10)