SOLUTION: |4y-9| >7

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Question 635546: |4y-9| >7
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
abs%284y-9%29%3E7 Start with the given inequality


Break up the absolute value (remember, if you have abs%28x%29%3E+a, then x+%3C+-a or x+%3E+a)

4y-9+%3C+-7 or 4y-9+%3E+7 Break up the absolute value inequality using the given rule




Now lets focus on the first inequality 4y-9+%3C+-7


4y-9%3C-7 Start with the given inequality


4y%3C-7%2B9Add 9 to both sides


4y%3C2 Combine like terms on the right side


y%3C%282%29%2F%284%29 Divide both sides by 4 to isolate y



y%3C1%2F2 Reduce


Now lets focus on the second inequality 4y-9+%3E+7


4y-9%3E7 Start with the given inequality


4y%3E7%2B9Add 9 to both sides


4y%3E16 Combine like terms on the right side


y%3E%2816%29%2F%284%29 Divide both sides by 4 to isolate y



y%3E4 Divide



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Answer:

So our answer is

y+%3C+1%2F2 or y+%3E+4


which looks like this in interval notation





if you wanted to graph the solution set, you would get

Graph of the solution set in blue and the excluded values represented by open circles