Solution set? lz+3l=lz-8l
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Solution set? lz+3l=lz-8l

[From: ] [author: ] [Date: 11-05-09] [Hit: ]
-.How do I start to solve this problem? I need to know how to do it.Thank you, any help is appreciated.I dont think this is an empty set.......
I have no clue on how to solve this problem. I cannot get it right. -.-
the problem is:
z+3=z-8

How do I start to solve this problem? I need to know how to do it.
Thank you, any help is appreciated.
I don't think this is an empty set.

-
Break this into cases for z < -3 and z > -3. Clearly z = -3 is not a solution.

1) z < -3.

Now we have |z + 3| = z + 3 and |z - 8| = z - 8 where z is negative, so in this case,

z + 3 > z - 8 and there are no answers where z < -3.
-----------------

2) z > -3. Add 3 to both sides and you get z + 3 > 0

Now look at z - 8. From z - 3 > 0 above add 5 to both sides and we get z + 3 > 5

Since z + 3 = z + 3, take (5 - 0) and divide the difference by 2, getting 2.5

That should be your answer. Let's check it.

|2.5 + 3| = 5.5

|2.5 - 8| = |-5.5| = 5.5|

So for z = 2.5, |z + 3| = |z - 8|

ONLY ANSWER: z = 2.5

.

-
|z + 3| = |z - 8|
square the both sides
(z+3)^2 = (z-8)^2
z^2 +6z +9 = z^2 -16z +64
22z = 55
z = 5/2
1
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