SOLUTION: solve this inequality and check your solution. then graph the solution on a number line. 2n+5>11-n

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Question 164315: solve this inequality and check your solution. then graph the solution on a number line. 2n+5>11-n
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
2n%2B5%3E11-n Start with the given inequality.


2n%3E11-n-5 Subtract 5 from both sides.


2n%2Bn%3E11-5 Add n to both sides.


3n%3E11-5 Combine like terms on the left side.


3n%3E6 Combine like terms on the right side.


n%3E%286%29%2F%283%29 Divide both sides by 3 to isolate n.


n%3E2 Reduce.


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Answer:

So the answer is n%3E2



So the answer in interval notation is


Also, the answer in set-builder notation is


Check:

To check the answer, simply plug in a value that is greater than 2 (say 3)

2n%2B5%3E11-n Start with the given inequality.


2%283%29%2B5%3E11-3 Plug in n=3


6%2B5%3E11-3 Multiply


11%3E8 Combine like terms. Since the inequality is true, this verifies our answer.


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Here's the graph of the solution set



Take note of the open circle at n=2. This tells us to exclude the endpoint.