SOLUTION: Can anyone solve the following? 27< 4|y + 9|-9 Thanks so much

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Question 43104: Can anyone solve the following?
27< 4|y + 9|-9


Thanks so much
Found 2 solutions by fractalier, AnlytcPhil:
Answer by fractalier(6550) About Me  (Show Source):
You can put this solution on YOUR website!
We first wish to isolate the absolute value...so we get
27 < 4|y + 9| - 9
36 < 4|y + 9|
9 < |y + 9| or
|y + 9| > 9
Now we break this up into two separate inequalities...one is exactly the way you see it without the absolute value sign and the second one you reverse both the inequality sign and the sign of the right hand side...so we have...
y + 9 > 9 and y + 9 < -9 and then
y > 0 and y < -18

Answer by AnlytcPhil(1807) About Me  (Show Source):
You can put this solution on YOUR website!
Can anyone solve the following?

                27 < 4|y + 9| - 9

You must learn two principles for 
inequalities to remove the absolute
value bars:
-----------------------------------
1. If C > 0
              |Ax + B| < C

   can be rewritten as

         " -C < Ax + B < C " 
-----------------------------------
2. If C > 0

              |Ax + B| > C

   can be rewritten as

   "  Ax + B < -C OR  Ax + B > C  "

------------------------------------  
Note the above two principles also 
hold for < and >          

    -4|y + 9| + 27 < -9

         -4|y + 9| < -9 - 27

         -4|y + 9| < -36

Divide both sides by -4, which reverses
the inequality:

           |y + 9| > 9 

This is principle 2 above

    y + 9 < -9  OR y + 9 > 9

        y < -18 OR y > 0

Plot on a numberline:

 <======o-----------o======>   
      -18           0

Interval notation:

      (-¥, -18) È (0, ¥)  

Edwin
AnlytcPhil@aol.com