SOLUTION: can you help me solve this problem Solve and write the answer in set notation /3x-6/>3 Here is my answer 3x-6>3 3x-6>-3 3x-6+6>3+6 3x-6+6>-3+6 3x>9 3x>

Solve and write the answer in set notation
|3x-6|>3 
Here is my answer
3x-6>3 3x-6>-3
3x-6+6>3+6 3x-6+6>-3+6
3x>9 3x>3
3x/3>9/3=x>3 3x/3>3/3=x>1 
{x/x>3}

No that's wrong.  You can't solve absolute value
inequalities the same way you solve absolute
value equations.

Learn these two rules, one for < and one for >:

1.  To remove absolute values from

|EXPRESSION| < A

Change it to

-A < EXPRESSION < +A

and solve for x in the middle

2.  To remove absolute values from

|EXPRESSION| > A

Change it to

EXPRESSION < -A  OR EXPRESSION > +A

and solve both parts for x.


Yours is case 2:

|3x - 6| > 3

Change it to

3x - 6 < -3 OR 3x - 6 > +3
    3x < 3  OR     3x > 9
     x < 1  OR      x > 3

So you can write this in set-builder
notation as

{x | x < 1 OR x > 3}

You can also write it in interval notation

  (-¥, 1) È (3, ¥)

Edwin