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

The solution to 3/(2x-1)>= 5/(x-1) is x<= 2/7 \lor 1/2 <x<1

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

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

x \leq \frac{2}{7} or \frac{1}{2} < x < 1

Interval Notation

(- \infty, \frac{2}{7}] \cup (\frac{1}{2}, 1)

Decimal Notation

x \leq 0.28571 \dots or 0.5 < x < 1

Solution steps

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

Rewrite in standard form

\frac{- 7 x + 2}{( x - 1 ) ( 2 x - 1 )} \geq 0

Identify the intervals

x \leq \frac{2}{7} or \frac{1}{2} < x < 1

\frac{1}{x} - 2 - \frac{1}{x} \leq \frac{2}{x} + 2

(x^{2} - 3 x + 2) (x^{3} - 3 x^{2}) (4 - x^{2}) \geq 0

\frac{( x ^{2} - 5 x + 4 )}{( x - 4 )} \geq 0

x^{3} < 7 x + 6

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

What is 3/(2x-1)>= 5/(x-1) ?
The solution to 3/(2x-1)>= 5/(x-1) is x<= 2/7 \lor 1/2 <x<1