SOLUTION: How would I solve abs((3x-7)/(x-4)) < 5

Algebra ->  Absolute-value -> SOLUTION: How would I solve abs((3x-7)/(x-4)) < 5      Log On


   

Question 509640: How would I solve
abs((3x-7)/(x-4)) < 5
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
abs((3x-7)/(x-4)) < 5
|(3x-7)/(x-4)| < 5
solve for (3x-7)/(x-4)>0
(3x-7)/(x-4) < 5
3x-7<5x-20
-2x<-14
x>7
..
solve for (3x-7)/(x-4)<0
(-3x+7)/(x-4) < 5
-3x+7<5x-20
-8x<-27
x<27/8
...
solution:
(-∞, 27/8) U (7, ∞)