How do you solve #|x-1|+|x+1|=2+x#?

1 Answer
May 1, 2016

Answer:

#x=-4, -2/3, 0 and 2#

Explanation:

#|(a+b|# is the combined expression for the pair #+-(a+b)#.

So, the given equation is ta single combined equation for the foue separate equations

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

Writing each equation, choosing prefixing signs as #(+ +). (+ -), (- +) and (- -)#, and solve. The solutions in this order are

.#x=2, -4, 0 and -2/3#.