SOLUTION: solve and graph absolute value inequality. write solution in interval notation /8x-1/-1>2

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Question 337765: solve and graph absolute value inequality. write solution in interval notation
/8x-1/-1>2
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

abs%288x-1%29-1%3E2 Start with the given inequality


abs%288x-1%29%3E3 Add 1 to both sides.


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

8x-1+%3C+-3 or 8x-1+%3E+3 Break up the absolute value inequality using the given rule




Now lets focus on the first inequality 8x-1+%3C+-3


8x-1%3C-3 Start with the given inequality


8x%3C-3%2B1Add 1 to both sides


8x%3C-2 Combine like terms on the right side


x%3C%28-2%29%2F%288%29 Divide both sides by 8 to isolate x



x%3C-1%2F4 Reduce


Now lets focus on the second inequality 8x-1+%3E+3


8x-1%3E3 Start with the given inequality


8x%3E3%2B1Add 1 to both sides


8x%3E4 Combine like terms on the right side


x%3E%284%29%2F%288%29 Divide both sides by 8 to isolate x



x%3E1%2F2 Reduce



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Answer:

So our answer is

x+%3C+-1%2F4 or x+%3E+1%2F2


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



If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website.

Jim