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

May 1, 2016

$x = - 4 , - \frac{2}{3} , 0 \mathmr{and} 2$

Explanation:

|(a+b| is the combined expression for the pair $\pm \left(a + b\right)$.

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

$\pm \left(x - 1\right) \pm \left(x + 1\right) = x + 2$.

Writing each equation, choosing prefixing signs as $\left(+ +\right) . \left(+ -\right) , \left(- +\right) \mathmr{and} \left(- -\right)$, and solve. The solutions in this order are

.$x = 2 , - 4 , 0 \mathmr{and} - \frac{2}{3}$.