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...

Algebra ->  Absolute-value -> 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...      Log On


   

Question 100610: 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...
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
2%2Aabs%282x-3%29%2B12%3E14 Start with the given inequality


2%2Aabs%282x-3%29%3E2 Subtract 12 from both sides.


abs%282x-3%29%3E2 Divide both sides by 2



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

2x-3+%3C+-1 or 2x-3+%3E+1 Break up the absolute value inequality using the given rule




Now lets focus on the first inequality 2x-3+%3C+-1


2x-3%3C-1 Start with the given inequality


2x%3C-1%2B3Add 3 to both sides


2x%3C2 Combine like terms on the right side


x%3C%282%29%2F%282%29 Divide both sides by 2 to isolate x



x%3C1 Divide


Now lets focus on the second inequality 2x-3+%3E+1


2x-3%3E1 Start with the given inequality


2x%3E1%2B3Add 3 to both sides


2x%3E4 Combine like terms on the right side


x%3E%284%29%2F%282%29 Divide both sides by 2 to isolate x



x%3E2 Divide



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Answer:

So our answer is

x+%3C+1 or x+%3E+2


which means the answer in set builder notation is




which looks like this in interval notation