SOLUTION: 120. Solve and match your result to the correct answer below. -10 < 30 - 8m is < or equal to 6

Algebra ->  Algebra  -> Inequalities -> SOLUTION: 120. Solve and match your result to the correct answer below. -10 < 30 - 8m is < or equal to 6      Log On

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Question 150799: 120. Solve and match your result to the correct answer below.
-10 < 30 - 8m is < or equal to 6
Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
-10+%3C+30+-+8m+%3C=+6 Start with the given compound inequality.


-10-30%3C-8m%3C=6-30 Subtract 30 from all sides.


-40%3C-8m%3C=6-30 Combine like terms on the left side.


-40%3C-8m%3C=-24 Combine like terms on the right side.


%28-40%29%2F%28-8%29%3Em%3E=%28-24%29%2F%28-8%29 Divide all sides by -8. This flips the inequality signs


5%3Em%3E=3 Divide.


3%3C=m%3C5 Rearrange the inequality.



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Answer:

So the solution is 3%3Cm%3C=5



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-2%2C+10%2C-10%2C+10%2C%0D%0Anumber_line%28+500%2C+-2%2C+10+%2C3%29%2C%0D%0A%0D%0Ablue%28line%283%2C0%2C5%2C0%29%29%2C%0D%0Ablue%28line%283%2C0.30%2C5%2C0.30%29%29%2C%0D%0Ablue%28line%283%2C0.15%2C5%2C0.15%29%29%2C%0D%0Ablue%28line%283%2C-0.15%2C5%2C-0.15%29%29%2C%0D%0Ablue%28line%283%2C-0.30%2C5%2C-0.30%29%29%2C%0D%0Acircle%285%2C0%2C0.25%29%2C%0D%0Acircle%285%2C0%2C0.20%29%0D%0A%0D%0A%29 Graph of the solution set

Note:
There is a closed circle at m=3 which means that we're including this value in the solution set
Also, there is an open circle at m=5 which means that we're excluding this value from the solution set.