SOLUTION: Solve the inequality, and express the solutions in terms of intervals whenever possible. (Enter your answer using interval notation. If there is no solution, enter NO SOLUTION.)

Algebra ->  Absolute-value -> SOLUTION: Solve the inequality, and express the solutions in terms of intervals whenever possible. (Enter your answer using interval notation. If there is no solution, enter NO SOLUTION.)       Log On


   

Question 709355: Solve the inequality, and express the solutions in terms of intervals whenever possible. (Enter your answer using interval notation. If there is no solution, enter NO SOLUTION.)
4 < |3x − 3| < 5
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Two possiblilities to check. One is if 3x-3>=0 and the other is for 3x-3<0. Before going into more, factor the expression..
3x-3=3%28x-1%29. Take care of that in the inequality statement.

4 < |3x − 3| < 5
4%3C3abs%28x-1%29%3C5
4%2F3+%3C+abs%28x-1%29+%3C+5%2F3

If x-1%3E=0 then:
4%2F3+%3C+x-1+%3C+5%2F3
4%2F3%2B1+%3C+x+%3C+5%2F3%2B1
7%2F3+%3C+x+%3C+8%2F3

If x-1<0 then :
4%2F3+%3C+1-x+%3C+5%2F3
4%2F3-1+%3C+-x+%3C+5%2F3-1
1%2F3+%3C+-x+%3C+2%2F3
Now multiply all members by NEGATIVE 1 and reverse the direction of the order symbols.
-1%2F3+%3E+x+%3E+-2%2F3
And to keep lesser to the left and greater to the right,
-2%2F3+%3C+x+%3C+-1%2F3

FINAL RESULT STATEMENT: -2%2F3+%3C+x+%3C+-1%2F3 OR 7%2F3+%3C+x+%3C+8%2F3