Question 155132: 1. Solve:|x-1|+|x|+|x+1|=x+2
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 1. Solve:|x-1|+|x|+|x+1|=x+2
----------------------------------
The absolute terms change meaning depending on whether the variable
expression is positive or negative.
---------------
So determine the "zeroes" of the expressions:
x = 1, or x=0, or x=-1,
-----------------------------
Draw a number line and mark -1, 0, and 1,
------------------------------------------
Solve the equation for each of the resulting four intervals.
-------------------------
If x < -1 you get: 1-x -x -x-1 = x+2 ; -4x = 2; x = -1/2
But x=-1/2 is not less than -1 so no solution.
---------------------------
If -1 < x <0 you get: 1-x -x +x+1 = x+2; -x+2 = x+2; x = 0
But x=0 is not in (-1,0) so no solution.
---------------------------
If 0 < x < 1 you get: 1-x + x + x + 1 = x + 2; x+2 = x+2
That is true for all x in (0,1)
-------------------------------------
If 1
But x=1 is not in (1,+inf) so no solution
-----------------------------------------------
Final Answer: 0 < x < 1
===========================
Cheers,
Stan H.
|
|
|
