What is (((2x+1)(x+4)))/((x^2))>= 0 ?

The solution to (((2x+1)(x+4)))/((x^2))>= 0 is x 0

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(((2x+1)(x+4)))/((x^2))>= 0

\frac{( ( 2 x + 1 ) ( x + 4 ) )}{( x ^{2} )} \geq 0

x \leq - 4 or - \frac{1}{2} \leq x < 0 or x > 0

Interval Notation

(- \infty, - 4] \cup [- \frac{1}{2}, 0) \cup (0, \infty)

Decimal

x \leq - 4 or - 0.5 \leq x < 0 or x > 0

Solution steps

\frac{( 2 x + 1 ) ( x + 4 )}{x ^{2}} \geq 0

Identify the intervals

x \leq - 4 or - \frac{1}{2} \leq x < 0 or x > 0

(x^{2} - 16) \cdot (x^{2} - 4) < 0

(x - 2) (x - 2) - 15 < x - 2 + x - 2

3 x^{2} - 4 < 5

\frac{( a - 1 )}{a} > 0

x (x - 1) > 6

What is (((2x+1)(x+4)))/((x^2))>= 0 ?
The solution to (((2x+1)(x+4)))/((x^2))>= 0 is x<=-4\lor-1/2 <= x<0\lor x>0