SOLUTION: |2x-6| -2 < 2

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Question 180808: |2x-6| -2 < 2
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

abs%282x-6%29-2%3C2 Start with the given inequality


abs%282x-6%29%3C4 Add 2 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)

2x-6+%3E+-4 and 2x-6+%3C+4 Break up the absolute value inequality using the given rule


-4+%3C+2x-6+%3C+4 Combine the two inequalities to get a compound inequality



2+%3C+2x+%3C+10 Add 6 to all sides


1+%3C+x+%3C+5 Divide all sides by 2 to isolate x



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Answer:

So our answer is

1+%3C+x+%3C+5



which looks like this in interval notation





Also, the answer in set-builder notation is