What is 1/(2x-1)<= x ?

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1/(2x-1)<= x

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

- \frac{1}{2} \leq x < \frac{1}{2} or x \geq 1

Solution steps

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

Rewrite in standard form

\frac{1 - x ( 2 x - 1 )}{2 x - 1} \leq 0

Factor

\frac{1 - x ( 2 x - 1 )}{2 x - 1} : \frac{- ( x - 1 ) ( 2 x + 1 )}{2 x - 1}

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

Multiply both sides by

- 1

(reverse the inequality)

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

Simplify

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

Identify the intervals

- \frac{1}{2} \leq x < \frac{1}{2} or x \geq 1

- \frac{1}{5} + \frac{1}{2}

x^{3} + x^{2} - 16 x - 16

- \frac{1}{2} (- 2)^{2}

\frac{1}{3} (x - 1)^{2} = 12

(- 7)^{4}

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