I just wanted to plot a simple inequality: $$-x \geq 4$$ and wolframalpha gives me the following plot:
But I think it should look like this:
Am I correct? If so why is wolframalpha producing such plots?
N.B. To reproduce the plot, enter $\textit{plot -x >= 4}$ at the wolframalpha website.

As a rule of thumb, Wolfram Alpha is right.
The plot by Alpha shows the graph of the two functions $f(x)=-x$ and $g(x)=4$ to let you compare them visually.
It has no reason to show a $XY$ map of the Boolean function $-x\ge4$, as there is no $y$ variable.