How to Calculate Answer

Question

|x-1|+|x|+|x+1|=2

Answer 1

We need to break this into several cases using the zeroes for each absolute value.

 

For |x-1| the zero occurs at x = 1

For |x| the zero occurs at x = 0

For |x+1| the zero occurs at x = -1

 

First, let's let x ≤ -1:

 

|x - 1| + |x| + |x + 1| = 2

- (x -1 ) + (-x) + [-(x+1)] = 2

x - 1 + x + x + 1 = -2

3x = -2

x = -2/3 ....but we said x ≤ -1, so this is not a solution

 

Let -1 ≤ x ≤ 0:

|x - 1| + |x| + |x + 1| = 2

-(x - 1) - x + (x + 1) = 2

-x + 1 - x + x + 1 = 2

-x + 2 = 2

x = 0 ...which is in our bounds, so x = 0 is a solution

 

You can also do this procedure for 0 < x ≤ 1 and x > 1.  I believe that x = 0 is going to be the only solution though.

 

 

J.T.