Adding the sum of absolute values must be equal to 1 as a Constr with a linear solver

Question

I have a big problem with Constr.

i was:

$$\min \sum \sigma_{x_i}$$ $$s.t \sum x_i = 1, where \space \space0<= x_i<=1$$

and now I need that problem to be:

$$\min \sum \sigma_{x_i}$$ $$s.t \sum |x_i| = 1, where -1<= x_i<=1$$

how to transform that absolute value constraint in a linear constraint?