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