SOLUTION: solve and graph 3x+18 greater than equal to 9 and 3x-18 greater than equal to -15

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Question 146780: solve and graph
3x+18 greater than equal to 9 and 3x-18 greater than equal to -15
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Let's solve the first inequality 3x%2B18%3E=9:


3x%2B18%3E=9 Start with the first inequality.


3x%3E=9-18 Subtract 18 from both sides.


3x%3E=-9 Combine like terms on the right side.


x%3E=%28-9%29%2F%283%29 Divide both sides by 3 to isolate x.


x%3E=-3 Reduce.


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Now let's solve the second inequality 3x-18%3C=-15:


3x-18%3C=-15 Start with the second inequality.


3x%3C=-15%2B18 Add 18 to both sides.


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


x%3C=%283%29%2F%283%29 Divide both sides by 3 to isolate x.


x%3C=1 Reduce.


So our answer is x%3E=-3 and x%3C=1. The answer could be rearranged to -3%3C=x and x%3C=1 and then condensed to -3%3C=x%3C=1



So the answer in interval notation is []


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=-3 which means that we're including this value in the solution set
Also, there is a closed circle at x=1 which means that we're including this value in the solution set.