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!!!

Algebra ->  Equations -> 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!!!      Log On


   

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) About Me  (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) About Me  (Show Source):
You can put this solution on YOUR website!
abs%283x-6%29%3E3 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)

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




Now lets focus on the first inequality 3x-6+%3C+-3


3x-6%3C-3 Start with the given inequality


3x%3C-3%2B6Add 6 to both sides


3x%3C3 Combine like terms on the right side


x%3C%283%29%2F%283%29 Divide both sides by 3 to isolate x



x%3C1 Divide


Now lets focus on the second inequality 3x-6+%3E+3


3x-6%3E3 Start with the given inequality


3x%3E3%2B6Add 6 to both sides


3x%3E9 Combine like terms on the right side


x%3E%289%29%2F%283%29 Divide both sides by 3 to isolate x



x%3E3 Divide



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

Answer:

So our answer is

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

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