SOLUTION: 21-4|2-5w|>13 I have tried this problem over and over but I just end up getting more confused.

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Question 946696: 21-4|2-5w|>13 I have tried this problem over and over but I just end up getting more confused.
Found 3 solutions by Alan3354, josgarithmetic, MathTherapy:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
21-4|2-5w|>13
---
Subtract 21
-4|2-5w|> -8
Divide by 4
-|2-5w|> -2
Divide by -1 (changes polarity)
|2-5w| < 2
----
Case 1:
2-5w < 2
-5w < 0
w > 0
=============
Case 2:
-(2-5w) < 2
5w-2 < 2
5w < 4
w < 4/5

Answer by josgarithmetic(39623) About Me  (Show Source):
You can put this solution on YOUR website!
Simplify up to isolating the absolute value.

-4abs%282-5w%29%3E13-21
4abs%282-5w%29%3C21-13
4abs%282-5w%29%3C7
abs%282-5w%29%3C7%2F4

Think logically about the meaning of absolute value for the expression in the absolute value function. Either 2-5w is non-negative or it is negative. Analyze for both cases.

2-5w%3E=0:
-
abs%282-5w%29=2-5w%3C7%2F4
-5w%3C7%2F4-2
5w%3E2-7%2F4
5w%3E1%2F4
highlight%28w%3E1%2F20%29

2-5w%3C0:
-
abs%282-5w%29=-2%2B5w%3C7%2F4
5w%3C7%2F4%2B2
5w%3C15%2F4
w%3C%2815%2F4%29%281%2F5%29
highlight%28w%3C3%2F4%29

The solution satisfying both conditions will be the intersection of those:
highlight%281%2F20%3Cw%3C3%2F4%29

Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!

21-4|2-5w|>13 I have tried this problem over and over but I just end up getting more confused.
highlight_green%28system%28w+%3E+0_or%2Cw+%3C+4%2F5%29%29         

You can do the check!! 

===================

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