# How would you graph the inequality x > -4?

Apr 3, 2015

It depends on where you want to solve it.

If you're using real numbers, then $x > - 4$ explains itself pretty clearly: you must consider all the numbers greater than $- 4$.

If you're solving it on the plan, you'll notice that you have no conditions on the $y$ coordinate. So, any point of the plain whose $x$ coordinate is greater than $- 4$ is a solution, no matter which value its $y$ coordinate has.

For example, take the value $3$. It is greater than $- 4$, so every point in the plan with $x$ coordinate equal to $3$ is solving the equation. But all the points of the form $\left(3 , y\right)$ form the vertical line passing through $\left(3 , 0\right)$.

I hope that it is clear at this time that the solution of $x > - 4$, if interpreted in the plan, is the part of the plan "at the right" of the vertical line $x = - 4$, as shown in the plot:

graph{x> -4 [-4.854, 5.146, -2.02, 2.98]}