SOLUTION: Solve the compound inequality |3x-9| < 15 AND |2x-3| > 5 (which reads "The absolute value of 3x-9 is less than or equal to 15. AND The absolute value of 2x-3 is greater than or equ

Algebra ->  Inequalities -> SOLUTION: Solve the compound inequality |3x-9| < 15 AND |2x-3| > 5 (which reads "The absolute value of 3x-9 is less than or equal to 15. AND The absolute value of 2x-3 is greater than or equ      Log On


   

Question 845846: Solve the compound inequality |3x-9| < 15 AND |2x-3| > 5 (which reads "The absolute value of 3x-9 is less than or equal to 15. AND The absolute value of 2x-3 is greater than or equal to 5" Give answer in interval notation.
When I solve for each I get as far as the first being -2<_|x|<_24 and that the 2nd is -4>_|x|>_2. X cannot be both greater than -2 and less than -4 so I think it would be an empty set? Thank you
Answer by tommyt3rd(5050) About Me  (Show Source):
You can put this solution on YOUR website!
1)
-15 < 3x-9 < 15
-15+9 < 3x < 15+9
-6 < 3x < 24
-2 < x < 8
(-2,8)

2)
2x-3 < -5 or 2x-3 > 5
2x < -2 or 2x > 8
x < -1 or x > 4
(-oo,-1)U(4,oo)


intersection:
(-2,-1) U (4,8)