SOLUTION: Solve and graph the solution set. x + 11 > –5

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Question 93203: Solve and graph the solution set.
x + 11 > –5
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
x%2B11%3E-5 Start with the given equation


x%3E-5-11 Subtract 11 from both sides




x%3E-16 Combine like terms -11 and -5 on the right side to get -16


So our answer is
x%3E+-16

Now lets graph the inequality x%3E+-16


Start with the given inequality:

x%3E-16

Set up a number line:
number_line%28500%2C-26%2C-6%29

Now plot the point x=-16 on the number line


number_line%28500%2C-26%2C-6%2C+-16%29


Now pick any test point you want, I'm going to choose x=0, and test the inequality x%3E-16


0%3E-16 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=-16 as the boundary.This means we shade everything to the right of the point x=-16 like this
Graph of x%3E-16 with the shaded region in blue
note: at the point x=-16, there is an open circle. This means the point x=-16 is excluded from the solution set.