SOLUTION: Given f(x)=|x+5| ,find all values of x such that f(x) is greater than 8 . Write your answer in interval notation.

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Question 350698: Given f(x)=|x+5| ,find all values of x such that f(x) is greater than 8 . Write your answer in interval notation.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
We essentially want to solve abs%28x%2B5%29%3E8


abs%28x%2B5%29%3E8 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)

x%2B5+%3C+-8 or x%2B5+%3E+8 Break up the absolute value inequality using the given rule




Now lets focus on the first inequality x%2B5+%3C+-8


x%2B5%3C-8 Start with the given inequality


x%3C-8-5Subtract 5 from both sides


x%3C-13 Combine like terms on the right side


Now lets focus on the second inequality x%2B5+%3E+8


x%2B5%3E8 Start with the given inequality


x%3E8-5Subtract 5 from both sides


x%3E3 Combine like terms on the right side



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Answer:

So our answer is

x+%3C+-13 or x+%3E+3


which looks like this in interval notation




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

Also, feel free to check out my tutoring website

Jim