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Popular >

6/x <= x-5

Solution

\frac{6}{x} \leq x - 5

Solution

- 1 \leq x < 0 or x \geq 6

+1

Interval Notation

[- 1, 0) \cup [6, \infty)

Solution steps

\frac{6}{x} \leq x - 5

Rewrite in standard form

\frac{6 + 5 x - x ^{2}}{x} \leq 0

Factor

\frac{6 + 5 x - x ^{2}}{x} : \frac{- ( x + 1 ) ( x - 6 )}{x}

\frac{- ( x + 1 ) ( x - 6 )}{x} \leq 0

Multiply both sides by

- 1

(reverse the inequality)

\frac{( - ( x + 1 ) ( x - 6 ) ) ( - 1 )}{x} \geq 0 \cdot (- 1)

Simplify

\frac{( x + 1 ) ( x - 6 )}{x} \geq 0

Identify the intervals

- 1 \leq x < 0 or x \geq 6

Popular Examples

x^{2} + 4 x = - 4

simplify (1/10)^0 simplify

(\frac{1}{10})^{0}

simplify h/(sqrt(x+h)-\sqrt{x)}simplify

\frac{h}{x + h - x}

- 17 x = - 204

simplify (5^3)/4 simplify

\frac{5 ^{3}}{4}

Frequently Asked Questions (FAQ)

What is 6/x <= x-5 ?
The solution to 6/x <= x-5 is -1<= x<0\lor x>= 6