SOLUTION: x<-2

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Question 113926: x<-2
Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
Start with the given inequality:

x%3C-2

Set up a number line:
number_line%28500%2C-12%2C8%29

Now plot the point x=-2 on the number line


number_line%28500%2C-12%2C8%2C+-2%29


Now pick any test point you want, I'm going to choose x=0, and test the inequality x%3C-2


0%3C-2 Plug in x=0


Since this inequality is not true, we simply shade the entire portion that does not contain the point x=0 using the point x=-2 as the boundary. This means we shade everything to the left of the point x=-2 like this:
drawing%28500%2C50%2C-12%2C8%2C-10%2C10%2C%0D%0Anumber_line%28500%2C-12%2C8%29%2C%0D%0Acircle%28-2%2C-5.8%2C0.35%29%2C%0D%0Acircle%28-2%2C-5.8%2C0.4%29%2C%0D%0Acircle%28-2%2C-5.8%2C0.45%29%2C%0D%0Ablue%28line%28-2%2C-5%2C-2-10%2C-5%29%29%2C%0D%0Ablue%28line%28-2%2C-6%2C-2-10%2C-6%29%29%2C%0D%0Ablue%28line%28-2%2C-7%2C-2-10%2C-7%29%29%2C%0D%0Ablue%28arrow%28-2%2C-5%2C-2-10.2%2C-5%29%29%2C%0D%0Ablue%28arrow%28-2%2C-5.5%2C-2-10.2%2C-5.5%29%29%2C%0D%0Ablue%28arrow%28-2%2C-6%2C-2-10.2%2C-6%29%29%0D%0A%29 Graph of x%3C-2 with the shaded region in blue

note: at the point x=-2, there is an open circle. This means the point x=-2 is excluded from the solution set.