SOLUTION: How do I graph the inequality: x <= 5

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Question 110832: How do I graph the inequality: x <= 5
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
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 (simply draw a vertical line through x=5)
+graph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C+1000%28x-5%29%29+ graph of x=5
Now lets pick a test point, say (0,0). Any point will work, (just make sure the point doesn't lie on the line) but this point is the easiest to work with. Now evaluate the inequality x%3C=5 with the test point

Substitute (0,0) into the inequality
%280%29%3C=5 Plug in x=0 and y=0
0%3C=5 Simplify



(note: for some reason, some of the following images do not display correctly in Internet Explorer. So I would recommend the use of Firefox to see these images.)


Since this inequality is true, we simply shade the entire region that contains (0,0)
Graph of x%3C=5 with the boundary (which is the line x=5 in red) and the shaded region (in green)