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

1 Answer
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 #(3, y)# form the vertical line passing through #(3,0)#.

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]}