What is ((x^2+6))/((5x))>= 1 ?

The solution to ((x^2+6))/((5x))>= 1 is 0 = 3

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((x^2+6))/((5x))>= 1

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

0 < x \leq 2 or x \geq 3

Interval Notation

(0, 2] \cup [3, \infty)

Solution steps

\frac{x ^{2} + 6}{5 x} \geq 1

Rewrite in standard form

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

Factor

\frac{x ^{2} + 6 - 5 x}{x} : \frac{( x - 2 ) ( x - 3 )}{x}

\frac{( x - 2 ) ( x - 3 )}{x} \geq 0

Identify the intervals

0 < x \leq 2 or x \geq 3

\frac{4}{( ( x - 2 ) ^{2} )} > 1

(x^{2} - x) (x^{3} - x) (x^{4} - x) < 0

\frac{( x + 1 )}{( x ^{2} + 2 )} > \frac{1}{4}

x, f > 0

x^{3} + 6 x^{2} + 11 x + 6 > 0

What is ((x^2+6))/((5x))>= 1 ?
The solution to ((x^2+6))/((5x))>= 1 is 0<x<= 2\lor x>= 3