Linear equality in two variables equivalent to region below line? I'm studying high school algebra and we were posed this question:

Lester thinks that the solution of any inequality with a > sign is the
  region above the line and the solution of any inequality with a < sign
  is the region below the line. Is Lester correct? Explain why or why
  not.

Is this true? Or if it's not, can you please give me a counterexample?
 A: To be fair, you were given a very confusing question. "Any inequality" is clearly not even what your teacher meant, if this question is about linear inequalities in two variables. Did they mean any inequality of the form
$$ax + by + c < 0$$
for real numbers $a,b,c$?
It's true that
$$ax+by+c=0$$
is the equation of a line in the plane (in standard form) and that this line must partition the plane into a half-space where $ax+by+c$ is positive, and one where the expression is negative (since the value of $ax+by+c$ changes smoothly and is only zero when you touch the line). How can we tell whether the "top" or "bottom" half-space is the negative one? We can plug in a test point $(0,Y)$:
$$bY + c$$
and test what happens when $Y\to -\infty$: if $b>0$, the first term becomes more and more negative (while $c$ stays the same) so $bY+c$ is negative for sufficiently large $Y$; similarly when $b<0$ the expression becomes more and more positive.
So we can conclude that
$$ax+by+c < 0$$
describes a region below a line when $b>0$ and above a line when $b<0$ (when $b=0$ the line is vertical and "below" doesn't even make any sense.)
