Answer
$(-∞,0)$ U $(1, ∞)$
Work Step by Step
$x^2>x$
$x^2-x>x-x$
$x^2-x>0$
$x(x-1)>0$
$x>0$
$x-1>0$
$x-1+1>0+1$
$x>1$
We have three sections: $(-∞,0)$, $(0, 1)$, and $(1, ∞)$. We need to test one value for $x$ in each section to determine if the section would be a solution set. Since we have the > sign, we exclude the end points and use parentheses instead of brackets.
Let $x=-2$, $x=.5$, and $x=2$
$x=-2$
$x^2>x$
$(-2)^2>-2$
$4 > -2$ (true)
$x=.5$
$x^2>x$
$.5^2>.5$
$.25 > .5$ (false)
$x=2$
$x^2>x$
$(2)^2>2$
$4 > 2$ (true)
