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

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1/x >= x

Solution

\frac{1}{x} \geq x

x \leq - 1 or 0 < x \leq 1

Interval Notation

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

Solution steps

\frac{1}{x} \geq x

Rewrite in standard form

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

Factor

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

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

Multiply both sides by

- 1

(reverse the inequality)

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

Simplify

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

Identify the intervals

x \leq - 1 or 0 < x \leq 1

(2 - b) (1 + 2 b) + (1 + b) (b^{3} - 3 b)

- 13 x + 1 \leq - 25

(\frac{1}{4} a^{8} b^{4})^{2}

\frac{s}{4} - 1 = 3

0.1 + 2 (0.4 x + 1) = 12