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 ->  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


   

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<10 This question is from textbook

Answer by jim_thompson5910(35256) 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

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

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.