Answer
$(0$, infinity)
Work Step by Step
a number is $x$
a number's reciprocal is $1/x$
$2x+(1/x) \geq0$
Denominator is zero when $x=0$
$2x+(1/x) \geq0$
$2x+(1/x)= 0$
$2x=-1/x$
$2x*x=-1*x/x$
$2x^2=-1$
$2x^2/2=-1/2$
$x^2=-1/2$
$\sqrt {x^2} = \sqrt {-1/2}$
$x = \sqrt {-1/2}$
Since we have the square root of a negative number, this is not a real number (but instead an imaginary number).
(-infinity, $0)$
$(0$, infinity)
Let $x=-1$ and $x=1$
$x=-1$
$2x+(1/x) \geq0$
$2*-1+(1/-1) \geq0$
$-2 -1\geq0$
$-3 \geq 0$ (false)
$x=1$
$2x+(1/x) \geq0$
$2*1+(1/1) \geq0$
$2 + 1 \geq 0$
$3 \geq 0$ (true)
