SOLUTION: Solve this equation: |x+1| + |1-x| = 2 Thanks.

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Question 930503: Solve this equation:
|x+1| + |1-x| = 2
Thanks.

Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39623) About Me  (Show Source):
You can put this solution on YOUR website!
Analyze the equation logically. The absolute value inputs can be greater-than-or-equal to zero, or less than zero.


If both nonzero, then x%2B1%2B1-x=2
2=2; and you can find what must be x for both inputs to be nonzero.
x%2B1%3E=0
x%3E=-1
&
1-x%3E=0
1%3E=x
x%3C=1
Meaning:
highlight%28-1%3C=x%3C=1%29


IF both are negative, then -x-1%2B%28-1%29%2Bx=2
-2=2 FALSE statement. Obviously both expressions in the absolute value inputs must not be simultaneously negative.

If x+1>=0 and 1-x<0, then x%2B1%2B%28-1%29%2Bx=2
2x=2
x=1, which is only a piece of the solution found in -1%3C=x%3C=1.

If x+1<0 and 1-x>=0, then -x-1%2B1-x=2
-2x=2
x=-1, again this one is consistent with the first found inequality solution but is only one piece of it.

FINAL FINISHED ANSWER RESULT: highlight%28-1%3C=x%3C=1%29

Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!
Solve this equation:
|x+1| + |1-x| = 2
Thanks.
highlight_green%28-+1+%3C=+x+%3C=+1%29
You can do the check!!
===================
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