SOLUTION: Graph the inequality. x <= 5

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Question 85721: Graph the inequality.
x <= 5

Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
20.


Start with the given system of inequalities
x%3C=5



In order to graph this system of inequalities, we need to graph each inequality one at a time.

So lets graph the first inequality

In order to graph x%3C=5 we need to graph the equation x=5 (just replace the inequality sign with an equal sign). So lets graph the line x=5 (note: if you need help with graphing, check out this solver)
graph%28+400%2C+300%2C+-5%2C+10%2C+-10%2C+10%2C1000%28x-5000%2F1000%29%29 graph of x=5
Now lets pick a test point, say (0,0) (any point will work, but this point is the easiest to work with), and evaluate the inequality x%3C=5
%280%29%3C=5 Plug in x=0, y=0

0%3C=5 Simplify


Since this inequality is true, we shade the entire region containing (0,0)


drawing%28+400%2C+300%2C+-5%2C+10%2C+-10%2C+10%2Cgraph%28+400%2C+300%2C+-5%2C+10%2C+-10%2C+10%2C10000%28x-5000%2F1000%29%2C+10000%28x-5000%2F1000%2B0%29%29%2C%0D%0Agraph%28+400%2C+300%2C+-5%2C+10%2C+-10%2C+10%2C10000%28x-5000%2F1000%29%2C+10000%28x-5000%2F1000%2B0.75%29%29%2C%0D%0Agraph%28+400%2C+300%2C+-5%2C+10%2C+-10%2C+10%2C10000%28x-5000%2F1000%29%2C+10000%28x-5000%2F1000%2B1.5%29%29%2C%0D%0Agraph%28+400%2C+300%2C+-5%2C+10%2C+-10%2C+10%2C10000%28x-5000%2F1000%29%2C+10000%28x-5000%2F1000%2B2.25%29%29%2C%0D%0Agraph%28+400%2C+300%2C+-5%2C+10%2C+-10%2C+10%2C10000%28x-5000%2F1000%29%2C+10000%28x-5000%2F1000%2B3%29%29%2C%0D%0Agraph%28+400%2C+300%2C+-5%2C+10%2C+-10%2C+10%2C10000%28x-5000%2F1000%29%2C+10000%28x-5000%2F1000%2B3.75%29%29%2C%0D%0Agraph%28+400%2C+300%2C+-5%2C+10%2C+-10%2C+10%2C10000%28x-5000%2F1000%29%2C+10000%28x-5000%2F1000%2B4.5%29%29%2C%0D%0Agraph%28+400%2C+300%2C+-5%2C+10%2C+-10%2C+10%2C10000%28x-5000%2F1000%29%2C+10000%28x-5000%2F1000%2B5.25%29%29%2C%0D%0Agraph%28+400%2C+300%2C+-5%2C+10%2C+-10%2C+10%2C10000%28x-5000%2F1000%29%2C+10000%28x-5000%2F1000%2B6%29%29%2C%0D%0Agraph%28+400%2C+300%2C+-5%2C+10%2C+-10%2C+10%2C10000%28x-5000%2F1000%29%2C+10000%28x-5000%2F1000%2B6.75%29%29%2C%0D%0Agraph%28+400%2C+300%2C+-5%2C+10%2C+-10%2C+10%2C10000%28x-5000%2F1000%29%2C+10000%28x-5000%2F1000%2B7.5%29%29%2C%0D%0Agraph%28+400%2C+300%2C+-5%2C+10%2C+-10%2C+10%2C10000%28x-5000%2F1000%29%2C+10000%28x-5000%2F1000%2B8.25%29%29%2C%0D%0Agraph%28+400%2C+300%2C+-5%2C+10%2C+-10%2C+10%2C10000%28x-5000%2F1000%29%2C+10000%28x-5000%2F1000%2B9%29%29%2C%0D%0Agraph%28+400%2C+300%2C+-5%2C+10%2C+-10%2C+10%2C10000%28x-5000%2F1000%29%2C+10000%28x-5000%2F1000%2B9.75%29%29%29
Here is the graph of x%3C=5 with the graph of the line(x=5) in red and the shaded region in green
(note: In this case, the red line is a solid line. This means the boundaries are included in the region.)