Question

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

Answer 1

`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`.