Question

How do you graph the system of linear inequalities `x<5` and `x> -4`?

Answer 1

This inequality is read "X is less than 5 and X is greater than -4".

What this means is that we want to include every number between -4 and 5, but not -4 and 5 themselves. We can do this by drawing open circles at the points -4 and 5, and then connecting those two circles with a line.

This is the system of inequalities graphed on a number line:

Answer 2

Firstly, we are looking for the region where `x<5`, This region is independent of `y`, so we graph the region in two variables as follows in the `xy`-plane:

graph{(x-5)<0 [-10, 10, -5, 5]}

Secondly, we are looking for the region where `x>-4`, This region is also independent of `y`, so we graph the region in two variables as follows in the `xy`-plane:

graph{x>(-4) [-10, 10, -5, 5]}

If we want to simultaneously satisfy both inequalities then we require the union of these two regions, which is as follows:

graph{(x-5)(x+4)<0 [-10, 10, -5, 5]}