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Popular >

1/x >= x

Solution

\frac{1}{x} \geq x

Solution

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

+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

Popular Examples

simplify (2-b)(1+2b)+(1+b)(b^3-3b)simplify

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

- 13 x + 1 \leq - 25

simplify (1/4 a^8b^4)^2 simplify

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

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

0.1+2(0.4x+1)=12

0.1 + 2 (0.4 x + 1) = 12

Frequently Asked Questions (FAQ)

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