SOLUTION: hi. i need a answer for a couple inequalities. the directions are, solve each inequality. then graph the solution set. the inequalities are, 3<2x-3<15 and 4<2y-2<10

Algebra ->  Algebra  -> Inequalities -> SOLUTION: hi. i need a answer for a couple inequalities. the directions are, solve each inequality. then graph the solution set. the inequalities are, 3<2x-3<15 and 4<2y-2<10      Log On

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Question 175271This question is from textbook
: hi. i need a answer for a couple inequalities. the directions are, solve each inequality. then graph the solution set. the inequalities are, 3<2x-3<15 and 4<2y-2<10This question is from textbook

Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
I'm assuming that these are separate problems
# 1


3%3C2x-3%3C15 Start with the given compound inequality.


3%2B3%3C2x%3C15%2B3 Add 3 to all sides.


6%3C2x%3C15%2B3 Combine like terms on the left side.


6%3C2x%3C18 Combine like terms on the right side.


%286%29%2F2%3Cx%3C%2818%29%2F2 Divide all sides by 2.


3%3Cx%3C9 Reduce.


So the answer is 3%3Cx%3C9



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So the answer in interval notation is ()


Also, answer in set-builder notation is


Here's the graph of the solution set

drawing%28500%2C80%2C-2%2C+14%2C-10%2C+10%2C%0D%0Anumber_line%28+500%2C+-2%2C+14+%29%2C%0D%0A%0D%0Ablue%28line%283%2C0%2C9%2C0%29%29%2C%0D%0Ablue%28line%283%2C0.30%2C9%2C0.30%29%29%2C%0D%0Ablue%28line%283%2C0.15%2C9%2C0.15%29%29%2C%0D%0Ablue%28line%283%2C-0.15%2C9%2C-0.15%29%29%2C%0D%0Ablue%28line%283%2C-0.30%2C9%2C-0.30%29%29%2C%0D%0Acircle%283%2C0%2C0.25%29%2Ccircle%283%2C0%2C0.20%29%2C%0D%0Acircle%289%2C0%2C0.25%29%2C%0D%0Acircle%289%2C0%2C0.20%29%0D%0A%0D%0A%29 Graph of the solution set

Note:
There is an open circle at x=3 which means that we're excluding this value from the solution set
Also, there is an open circle at x=9 which means that we're excluding this value from the solution set.





# 2


4%3C2y-2%3C10 Start with the given compound inequality.


4%2B2%3C2y%3C10%2B2 Add 2 to all sides.


6%3C2y%3C10%2B2 Combine like terms on the left side.


6%3C2y%3C12 Combine like terms on the right side.


%286%29%2F2%3Cy%3C%2812%29%2F2 Divide all sides by 2.


3%3Cy%3C6 Reduce.


So the answer is 3%3Cy%3C6



---------------------------------------------------------------

So the answer in interval notation is ()


So the answer in set-builder notation is


Here's the graph of the solution set

drawing%28500%2C80%2C-2%2C+11%2C-10%2C+10%2C%0D%0Anumber_line%28+500%2C+-2%2C+11+%29%2C%0D%0A%0D%0Ablue%28line%283%2C0%2C6%2C0%29%29%2C%0D%0Ablue%28line%283%2C0.30%2C6%2C0.30%29%29%2C%0D%0Ablue%28line%283%2C0.15%2C6%2C0.15%29%29%2C%0D%0Ablue%28line%283%2C-0.15%2C6%2C-0.15%29%29%2C%0D%0Ablue%28line%283%2C-0.30%2C6%2C-0.30%29%29%2C%0D%0Acircle%283%2C0%2C0.25%29%2Ccircle%283%2C0%2C0.20%29%2C%0D%0Acircle%286%2C0%2C0.25%29%2C%0D%0Acircle%286%2C0%2C0.20%29%0D%0A%0D%0A%29 Graph of the solution set

Note:
There is an open circle at y=3 which means that we're excluding this value from the solution set
Also, there is an open circle at y=6 which means that we're excluding this value from the solution set.