SOLUTION: solve and graph the solution: 2(m-3) + 7 < 21

Algebra ->  Algebra  -> Inequalities -> SOLUTION: solve and graph the solution: 2(m-3) + 7 < 21      Log On

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Question 93536This question is from textbook
: solve and graph the solution:
2(m-3) + 7 < 21This question is from textbook

Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
2%28m-3%29+%2B+7+%3C+21

2m-6+%2B+7+%3C+21 Distribute


2m%2B7%3C21%2B6Add 6 to both sides



2m%2B7%3C27 Combine like terms on the right side


m%3C%2827%29%2F%282%29 Divide both sides by 2 to isolate m


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Answer:
So our answer is m%3C%2827%29%2F%282%29 which looks like m%3C13.5 in decimal form






Now lets graph the solution set of m%3C13.5

Set up a number line:
number_line%28500%2C3.5%2C23.5%29 note: just replace the x with the variable you are working with


Now plot the point m=13.5 on the number line


number_line%28500%2C3.5%2C23.5%2C+13.5%29


Now pick any test point you want, I'm going to choose m=0, and test the inequality m%3C13.5


0%3C13.5 Plug in m=0


Since this inequality is true, we simply shade the entire portion in which contains the point m=0 using the point m=13.5 as the boundary.This means we shade everything to the left of the point m=13.5 like this:
drawing%28500%2C50%2C3.5%2C23.5%2C-10%2C10%2C%0D%0Anumber_line%28500%2C3.5%2C23.5%29%2C%0D%0Acircle%2813.5%2C-5.8%2C0.35%29%2C%0D%0Acircle%2813.5%2C-5.8%2C0.4%29%2C%0D%0Acircle%2813.5%2C-5.8%2C0.45%29%2C%0D%0Ablue%28line%2813.5%2C-5%2C13.5-10%2C-5%29%29%2C%0D%0Ablue%28line%2813.5%2C-6%2C13.5-10%2C-6%29%29%2C%0D%0Ablue%28line%2813.5%2C-7%2C13.5-10%2C-7%29%29%2C%0D%0Ablue%28arrow%2813.5%2C-5%2C13.5-10.2%2C-5%29%29%2C%0D%0Ablue%28arrow%2813.5%2C-5.5%2C13.5-10.2%2C-5.5%29%29%2C%0D%0Ablue%28arrow%2813.5%2C-6%2C13.5-10.2%2C-6%29%29%0D%0A%29 Graph of m%3C13.5 with the shaded region in blue

note: at the point m=13.5, there is an open circle. This means the point m=13.5 is excluded from the solution set.