Question 230648
|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