Question 230648: find all x-y such that |x+y|=1
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! |x+y| = 1 means that:
If the expression (x+y) >= 0, then:
x + y = 1
this means that:
x = 1-y
Example:
Let y = 5
x = 1-5 = -4
|-4 + 5| = |1| = 1 which is true so this looks good.
We have so far:
x = 1-y when the expression (x+y) is greater than or equal to 0.
If the expression (x+y) < 0, then:
- (x+y) = 1
Multiply both sides of this by (-1) to get:
(x+y) = -1
this means that:
x = -1 - y
Example:
Let y = 5
This means that x = -1 - 5 = -6
If x = -6 and y = 5, we get:
(x+y) = (-6 + 5) = -1 < 0
We also get:
|x + y| = |-6 + 5| = 1 which becomes |-1| = 1 which becomes 1 = 1 so this is good.
Your solution should be, if I understand the problem correctly:
x = 1-y
or:
x = -1-y
Let's see how that holds up.
Let y be any number.
We'll try -5 and 5
When y = -5, x will be either:
1-(-5) = 6
or:
-1-(-5) = 4
If x = 6 and y = -5, then |x+y| = |6-5| = |1| = 1 which is good.
If x = 4 and y = -5, then |x+y| = |4 -5| = |-1| = 1 which is good.
When y = 5, x with be either:
1 - 5 = -4
or:
-1 - 5 = -6
If x = -5 and y = 5, then |x+y| = |-4 + 5| = |1| = 1 which is good.
If x = -6 and y = 5, then |x+y| = |-6 + 5| = |-1| = 1 which is good.
Your answer is:
x = 1-y
or:
x = -1-y
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