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
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
