Real numbers/Convergent sequence/Modulus/Exercise

Let ${}{\left(x_{n}\right)}_{n\in \mathbb {N} }$ be a convergent sequence of real numbers with limit equal to ${}x$. Prove that also the sequence

${\left(\vert {x_{n}}\vert \right)}_{n\in \mathbb {N} }$

converges, and specifically to ${}\vert {x}\vert$.

Create a solution