SOLUTION: 2|2x-3|+12>14 Write the answer in two ways 1. using set builder notation ("and or "or"). 2. using interval notation. Please help!! Thanks in advance...

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Start with the given inequality


Subtract 12 from both sides.


Divide both sides by 2



Break up the absolute value (remember, if you have , then or )

or Break up the absolute value inequality using the given rule




Now lets focus on the first inequality


Start with the given inequality


Add 3 to both sides


Combine like terms on the right side


Divide both sides by 2 to isolate x



Divide


Now lets focus on the second inequality


Start with the given inequality


Add 3 to both sides


Combine like terms on the right side


Divide both sides by 2 to isolate x



Divide



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Answer:

So our answer is

or


which means the answer in set builder notation is




which looks like this in interval notation