For simplicity, we'll use $y \neq x$.
$x$: ($±∞$) ($\mathbb{R}$)
$y$: ($±∞$) ($\mathbb{R}$)
$z$: ($±∞$) ($\mathbb{C}$)
I've learned that $y > x$ would be graphed as: $y > x$ and y < x: $y < x$
but, I have yet to see $y \neq x$. I assume it would be graphed with a dotted line as it cannot actually be equal to $x$, and that it would be both at the same time. Would this accurately show the inequal sign? "$\neq$" $y \neq x?$
Would give complex solutions too?
On
It would be everything BUT the dotted line though it is not common to graph relations involving $\neq$.
Think as follows $y=x$ describes all the points on that dotted line that is the set
$$ \{(x,y)\mid x=y,\quad x,y\in\mathbb{R}\} $$
$y\neq x$ would be the complement of that so all the points for which $y\neq x$
$$ \{(x,y)\mid x\neq y,\quad x,y\in\mathbb{R}\} $$
which are all the points "outside" that dotted line, the whole plain with the line $y=x$ removed.
Hope this helped
In your attached image, the graph of $y \neq x$ is all of $\mathbb R^2$ outside of the line where $y=x$.
The dark grey background color represents where $y\neq x$. It would extend to infinity in both the $x$ and $y$ directions. The dotted line represents where $y=x$ and is not part of the graph.