Absolutely absolute

Algebra Level 2

Find the minimum value of x+1+2+3+4\large \Bigg | \bigg | \Big | \big | x + 1 \big | + 2 \Big | + 3 \bigg | + 4 \Bigg | for real xx.

Notation: | \cdot | denotes the absolute value function.

Bonus: Generalize this.

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