SOLUTION: I was wondering if anyone knows how to solve |ax+b|<cx+d type questions by using cases and the number line to finish. I am personally struggling with the number line, I have half-f

Algebra ->  Absolute-value -> SOLUTION: I was wondering if anyone knows how to solve |ax+b|<cx+d type questions by using cases and the number line to finish. I am personally struggling with the number line, I have half-f      Log On


   

Question 875091: I was wondering if anyone knows how to solve |ax+b| Question: |2x−4|<6x
Case 1: x≤2
−2x+4<6x
x>12
Case 2:x>2
2x−4<6x
x>−1

Found 2 solutions by lwsshak3, rothauserc:
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
solve |ax+b| Question: |2x−4|<6x
case 1:
2x-4<6x
4x>-4
x>-1 (reject, does not check)
..
case 2:
-(2x-4)<6x
2x-4>-6x
8x>4
x>1/2

Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
-6x < 2x-4 < 6x
This is the pattern for <
Case 1) 2x-4 < 6x
-4x < 4
x > -1
Case 2) 2x-4 > -6x
8x > 4
x > 1/2
The intervals are (-1, infinity), (1/2, infinity) which can be combined into the interval (-1, infinity)