The solution to 1/x >x is x<-1\lor 0<x<1

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1/x >x

Solution

\frac{1}{x} > x

x < - 1 or 0 < x < 1

Interval Notation

(- \infty, - 1) \cup (0, 1)

Solution steps

\frac{1}{x} > x

Rewrite in standard form

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

Factor

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

\frac{- ( x + 1 ) ( x - 1 )}{x} > 0

Multiply both sides by

- 1

(reverse the inequality)

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

Simplify

\frac{( x + 1 ) ( x - 1 )}{x} < 0

Identify the intervals

x < - 1 or 0 < x < 1

3 ∣ 2 a - 5 ∣ = 21

z^{2} - 11 z - 12

\frac{1}{\frac{3}{3}}

\frac{x ( x + 2 )}{4 x ^{2} - 9} < \frac{1}{5}

64 x^{3} - y^{6}