Absolute value question help

Question

Find all the value(s) of “x” for which the equation is true: |x| = |x+1|

Answer 1

Hi Gnaris,

 

|x| = |x+1| means

 

x = (x + 1)  or  x = -(x + 1)

x = x + 1 is not possible. 

 

Let's check the other possible solution.

x = -(x + 1)

x = -x - 1

2x = -1

x = -1/2 is the solution.

 

 

Answer 2

The solution set is just x = -1/2.   The value x = -1/2 can be easily checked to be a solution.   A way to see that it is the only solution is to use a graphing calculator such as the TI-84.  Put abs(x) into Y1 and abs(x+1) into Y2.