SOLUTION: Please help me solve this inequality and graph soloution set 3 + x < -4 or 3 + x > 4

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Question 105326This question is from textbook Merrill Algebra One
: Please help me solve this inequality and graph soloution set
3 + x < -4 or 3 + x > 4 This question is from textbook Merrill Algebra One

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Which one is it? I'm assuming you want to solve the first inequality

3%2Bx%3C-4 Start with the given inequality


x%3C-4-3Subtract 3 from both sides


x%3C-7 Combine like terms on the right side


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Answer:
So our answer is x%3C-7



Now let's graph the solution set


Start with the given inequality:

x%3C-7

Set up a number line:
number_line%28500%2C-17%2C3%29

Now plot the point x=-7 on the number line


number_line%28500%2C-17%2C3%2C+-7%29


Now pick any test point you want, I'm going to choose x=0, and test the inequality x%3C-7


0%3C-7 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=-7 as the boundary. This means we shade everything to the left of the point x=-7 like this:
Graph of x%3C-7 with the shaded region in blue

note: at the point x=-7, there is an open circle. This means the point x=-7 is excluded from the solution set.