SOLUTION: -4<|6x-1|+4

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Question 777810: -4<|6x-1|+4
Found 2 solutions by jim_thompson5910, lwsshak3:
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
-4<|6x-1|+4

-4-4 < |6x-1|

-8 < |6x-1|

|6x - 1| > -8

Since the absolute value of any number is NEVER negative, this means that |6x-1| is ALWAYS larger than any negative number you can think of.

Therefore, |6x - 1| > -8 is ALWAYS true for ANY x value

So -4<|6x-1|+4 has infinitely many solutions and that means you can plug in any value for x and it will be true.

So again, there are infinitely many solutions and you can say the solution set is the set of real numbers.

Answer by lwsshak3(11628) (Show Source):
You can put this solution on YOUR website!
-4<|6x-1|+4
solve for 2 cases:
case 1
-4<6x-1+4
-7<6x
x>-7/6
..
case 2
-4<-6x+1+4
-6x>-9
6x<9
x<9/6=3/2
solution: (-7/6,3/2)