SOLUTION: Please help me solve and write interval notation for the solution set -4 less than or equal to 3x+1 less than 7 Thanks in advance!!!

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Question 162839: Please help me solve and write interval notation for the solution set
-4 less than or equal to 3x+1 less than 7
Thanks in advance!!!

Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
-4%3C=3x%2B1%3C7 Start with the given compound inequality.


-4-1%3C=3x%3C7-1 Subtract 1 from all sides.


-5%3C=3x%3C7-1 Combine like terms on the left side.


-5%3C=3x%3C6 Combine like terms on the right side.


%28-5%29%2F3%3C=x%3C%286%29%2F3 Divide all sides by 3 to isolate "x".


-5%2F3%3C=x%3C2 Reduce.


So the answer is -5%2F3%3C=x%3C2



So the answer in interval notation is [)


Note: remember, brackets include the endpoints while parenthesis exclude the endpoints.


Also the answer in set-builder notation is


Here's the graph of the solution set

drawing%28500%2C80%2C-10%2C+7%2C-10%2C+10%2C%0D%0Anumber_line%28+500%2C+-10%2C+7+%2C-5%2F3%29%2C%0D%0A%0D%0Ablue%28line%28-5%2F3%2C0%2C2%2C0%29%29%2C%0D%0Ablue%28line%28-5%2F3%2C0.30%2C2%2C0.30%29%29%2C%0D%0Ablue%28line%28-5%2F3%2C0.15%2C2%2C0.15%29%29%2C%0D%0Ablue%28line%28-5%2F3%2C-0.15%2C2%2C-0.15%29%29%2C%0D%0Ablue%28line%28-5%2F3%2C-0.30%2C2%2C-0.30%29%29%2C%0D%0Acircle%282%2C0%2C0.25%29%2C%0D%0Acircle%282%2C0%2C0.20%29%0D%0A%0D%0A%29 Graph of the solution set

Note:
There is a closed circle at x=-5%2F3 which means that we're including this value in the solution set
Also, there is an open circle at x=2 which means that we're excluding this value from the solution set.