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Popular >

1/x <= x

Solution

\frac{1}{x} \leq x

Solution

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

+1

Interval Notation

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

Solution steps

\frac{1}{x} \leq x

Rewrite in standard form

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

Factor

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

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

Multiply both sides by

- 1

(reverse the inequality)

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

Simplify

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

Identify the intervals

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

Popular Examples

simplify (5n)/(30m)+(2m+4n)/(30m)simplify

\frac{5 n}{30 m} + \frac{2 m + 4 n}{30 m}

simplify 11/6+9/2 simplify

\frac{11}{6} + \frac{9}{2}

∣ 2 g - 5 ∣ \geq 9

factor x^2-15x+44 factor

x^{2} - 15 x + 44

2 x = 5

Frequently Asked Questions (FAQ)

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