SOLUTION: |2a-6|>10

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Question 319141: |2a-6|>10
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

abs%282a-6%29%3E10 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)

2a-6+%3C+-10 or 2a-6+%3E+10 Break up the absolute value inequality using the given rule




Now lets focus on the first inequality 2a-6+%3C+-10


2a-6%3C-10 Start with the given inequality


2a%3C-10%2B6Add 6 to both sides


2a%3C-4 Combine like terms on the right side


a%3C%28-4%29%2F%282%29 Divide both sides by 2 to isolate a



a%3C-2 Divide


Now lets focus on the second inequality 2a-6+%3E+10


2a-6%3E10 Start with the given inequality


2a%3E10%2B6Add 6 to both sides


2a%3E16 Combine like terms on the right side


a%3E%2816%29%2F%282%29 Divide both sides by 2 to isolate a



a%3E8 Divide



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Answer:

So our answer is

a+%3C+-2 or a+%3E+8


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