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(35256) 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

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.