SOLUTION: Solve the inequality and graph the solution x - 5 < 3

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Question 117755: Solve the inequality and graph the solution
x - 5 < 3
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x-5%3C3 Start with the given inequality



x%3C3%2B5Add 5 to both sides


x%3C8 Combine like terms on the right side

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Answer:
So our answer is x%3C8






Now let's graph the solution set
Start with the given inequality:

x%3C8

Set up a number line:
number_line%28500%2C-2%2C18%29

Now plot the point x=8 on the number line


number_line%28500%2C-2%2C18%2C+8%29


Now pick any test point you want, I'm going to choose x=0, and test the inequality x%3C8


0%3C8 Plug in x=0


Since this inequality is true, we simply shade the entire portion in which contains the point x=0 using the point x=8 as the boundary.This means we shade everything to the left of the point x=8 like this:
Graph of x%3C8 with the shaded region in blue

note: at the point x=8, there is an open circle. This means the point x=8 is excluded from the solution set.