SOLUTION: 1/4(8y+4)-34<-1/3(9y-6)

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Question 178299: 1/4(8y+4)-34<-1/3(9y-6)
Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
%281%2F4%29%288y%2B4%29-34%3C-%281%2F3%29%289y-6%29 Start with the given inequality


3%288y%2B4%29-408%3C-4%289y-6%29 Multiply EVERY term (that's not in a set of parenthesis) by the LCD 12 to clear the fractions.


24y%2B12-408%3C-36y%2B24 Distribute.


24y-396%3C-36y%2B24 Combine like terms on the left side.


24y%3C-36y%2B24%2B396 Add 396 to both sides.


24y%2B36y%3C24%2B396 Add 36y to both sides.


60y%3C24%2B396 Combine like terms on the left side.


60y%3C420 Combine like terms on the right side.


y%3C%28420%29%2F%2860%29 Divide both sides by 60 to isolate y.


y%3C7 Reduce.


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Answer:

So the answer is y%3C7



So the answer in interval notation is


Also, the answer in set-builder notation is


Here's the graph of the solution set on the number line:

drawing%28500%2C80%2C-3%2C+17%2C-10%2C+10%2C%0D%0Anumber_line%28+500%2C+-3%2C+17%29%2C%0D%0A%0D%0A%0D%0Aarrow%287%2C0%2C-3%2C0%29%2C%0D%0Aarrow%287%2C0.30%2C-3%2C0.30%29%2C%0D%0Aarrow%287%2C0.15%2C-3%2C0.15%29%2C%0D%0Aarrow%287%2C-0.15%2C-3%2C-0.15%29%2C%0D%0Aarrow%287%2C-0.30%2C-3%2C-0.30%29%2C%0D%0A%0D%0A%0D%0A%0D%0A%0D%0Acircle%287%2C0%2C0.3%29%2C%0D%0Acircle%287%2C0%2C0.3%29%2C%0D%0Acircle%287%2C0%2C0.3%29%2C%0D%0Acircle%287%2C0%2C0.3-0.02%29%0D%0A%29