SOLUTION: Could you show how to solve and graph this inequality? I am a parent trying to help my son with 8th grade algebra. -7 < 3x + 2 is less than or equal to 14

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Question 182032: Could you show how to solve and graph this inequality? I am a parent trying to help my son with 8th grade algebra.
-7 < 3x + 2 is less than or equal to 14

Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!

-7%3C3x%2B2%3C=14 Start with the given compound inequality.


-7-2%3C3x%3C=14-2 Subtract 2 from all sides.


-9%3C3x%3C=14-2 Combine like terms on the left side.


-9%3C3x%3C=12 Combine like terms on the right side.


%28-9%29%2F3%3Cx%3C=%2812%29%2F3 Divide all sides by 3.


-3%3Cx%3C=4 Reduce.


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Answer:

So the solution is -3%3Cx%3C=4


So the answer in interval notation is (]


Also, the answer in set-builder notation is


Here's the graph of the solution set

drawing%28500%2C80%2C-8%2C+9%2C-10%2C+10%2C%0D%0Anumber_line%28+500%2C+-8%2C+9+%2C4%29%2C%0D%0A%0D%0Ablue%28line%28-3%2C0%2C4%2C0%29%29%2C%0D%0Ablue%28line%28-3%2C0.30%2C4%2C0.30%29%29%2C%0D%0Ablue%28line%28-3%2C0.15%2C4%2C0.15%29%29%2C%0D%0Ablue%28line%28-3%2C-0.15%2C4%2C-0.15%29%29%2C%0D%0Ablue%28line%28-3%2C-0.30%2C4%2C-0.30%29%29%2C%0D%0Acircle%28-3%2C0%2C0.25%29%2Ccircle%28-3%2C0%2C0.20%29%0D%0A%0D%0A%29 Graph of the solution set

Note:
There is an open circle at x=-3 which means that we're excluding this value from the solution set
Also, there is a closed circle at x=4 which means that we're including this value in the solution set.