Absolute Madness

Algebra Level 5

\[\displaystyle \sum_{k=1}^{n} |x_{k}|=19+\left|\sum_{k=1}^{n} x_{k}\right|\,.\]

If \(x_i\) is real,\(i\in\mathbb{N}\),such that \(|x_{i}|<1\).

What is the smallest possible value of \(n\) such that it satisfy the equation above?

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