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...

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) (Show Source): You can put this solution on YOUR website!
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

----------------------------------------------------

Answer:

So our answer is

or

which means the answer in set builder notation is

which looks like this in interval notation

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