SOLUTION: please solve this inequality and write the solutions as a compound inequality: |x-10|-9<-1

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Question 336211: please solve this inequality and write the solutions as a compound inequality: |x-10|-9<-1
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

abs%28x-10%29-9%3C-1 Start with the given inequality


abs%28x-10%29%3C8 Add 9 to both sides.


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

x-10+%3E+-8 and x-10+%3C+8 Break up the absolute value inequality using the given rule


-8+%3C+x-10+%3C+8 Combine the two inequalities to get a compound inequality



2+%3C+x+%3C+18 Add 10 to all sides


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Answer:

So our answer is

2+%3C+x+%3C+18



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 website.

Jim