en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

1/x <x

Solution

\frac{1}{x} < x

Solution

- 1 < x < 0 or x > 1

+1

Interval Notation

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

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

- 1 < x < 0 or x > 1

Popular Examples

x - 7 > 29

4 (2 - x) < - 6

9 > ∣ 4 - x ∣

factor 9m^6-36n^8 factor

9 m^{6} - 36 n^{8}

factor 2x^2(2x-4x^2)^2 factor

2 x^{2} (2 x - 4 x^{2})^{2}

Frequently Asked Questions (FAQ)

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