SOLUTION: Can a tutor help me please* My problem is to solve and write the answer in set notation: |3x-6|>3 Thank you, thank you, thank You!!!

Question 141091: Can a tutor help me please* My problem is to solve and write the answer in set notation: |3x-6|>3
Thank you, thank you, thank You!!!
Found 2 solutions by stanbon, jim_thompson5910:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
|3x-6|>3
------------
3x-6 > 3 or 3x-6 < -3
3x > 9 or 3x < 3
x > 3 or x < 1
---------------------------
Set Notation:
{x | x > 3} or {x | x < 1}
==============================
Cheers
Stan H.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given inequality

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 6 to both sides

Combine like terms on the right side

Divide both sides by 3 to isolate x

Divide

Now lets focus on the second inequality

Start with the given inequality

Add 6 to both sides

Combine like terms on the right side

Divide both sides by 3 to isolate x

Divide

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

Answer:

So our answer is

or

which in set notation is

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
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