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

Jul 8, 2017

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: Jul 10, 2017

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 $x y$-plane:

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

Secondly, we are looking for the region where $x \succ 4$, This region is also independent of $y$, so we graph the region in two variables as follows in the $x y$-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]}