SOLUTION: please tell me how to solve this problem. |y-2| = |y+3|

Question 50630This question is from textbook intermediate algebra
: please tell me how to solve this problem.
|y-2| = |y+3| This question is from textbook intermediate algebra

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
|y-2| = |y+3|
You need to know the following: |x|= x if x>=0; |x|=-x if x<0
Now you need to see that y-2 and y+3 can be positive or negative
depending on the value of "y"
Draw a number line and put the numbers -3 and 2 on the line
This segments the line into three segments.
We have to see where the solution of our problem lies.
Interval I is (-infinity,-3):
If y is in this interval both y-2 and y+3 will be negative so the equation reads will read 2-y=-y-3
Then -2=-3 which is impossible; so our solution is not in this interval.
----------
Interval II is (-3.2):
If y is in this interval y-2 will be negative and y+3 will be positive
so the equation will read 2-y=y+3
Then 2y=-1 and y=-1/2
That is a solution fot the equation.
------------
Interval III is (2, infinity):
If y is in this interal y-2 and y+3 will be positive so the equation
will read y-2=y+3.
The -2=3 which is impossible.
So there are no solutions in interval III.
--------------------
So the only solution is y=-1/2
Cheers,
Stan H.
y-2 and y+3 will be negative.
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