SOLUTION: How exactly do I solve a compound inequality such as -3<x+2<7?

Algebra ->  Algebra  -> Inequalities -> SOLUTION: How exactly do I solve a compound inequality such as -3<x+2<7?      Log On

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Question 165210: How exactly do I solve a compound inequality such as -3
Answer by jim_thompson5910(21684) About Me  (Show Source):
You can put this solution on YOUR website!
-3%3Cx%2B2%3C7 Start with the given compound inequality.


-3-2%3Cx%3C7-2 Subtract 2 from ALL sides.


-5%3Cx%3C7-2 Combine like terms on the left side.


-5%3Cx%3C5 Combine like terms on the right side.


So our answer is -5%3Cx%3C5


So the answer in interval notation is ()


So the answer in set-builder notation is


Here's the graph of the solution set

drawing%28500%2C80%2C-10%2C+10%2C-10%2C+10%2C%0D%0Anumber_line%28+500%2C+-10%2C+10+%29%2C%0D%0A%0D%0Ablue%28line%28-5%2C0%2C5%2C0%29%29%2C%0D%0Ablue%28line%28-5%2C0.30%2C5%2C0.30%29%29%2C%0D%0Ablue%28line%28-5%2C0.15%2C5%2C0.15%29%29%2C%0D%0Ablue%28line%28-5%2C-0.15%2C5%2C-0.15%29%29%2C%0D%0Ablue%28line%28-5%2C-0.30%2C5%2C-0.30%29%29%2C%0D%0Acircle%28-5%2C0%2C0.25%29%2Ccircle%28-5%2C0%2C0.20%29%2C%0D%0Acircle%285%2C0%2C0.25%29%2C%0D%0Acircle%285%2C0%2C0.20%29%0D%0A%0D%0A%29 Graph of the solution set

Note:
There is an open circle at x=-5 which means that we're excluding this value from the solution set
Also, there is an open circle at x=5 which means that we're excluding this value from the solution set.