Breaking a straight line

Algebra Level 3

The value of ∣ x − 1 ∣ + ∣ x − 2 ∣ + ∣ x − 3 ∣ + ∣ x − 4 ∣ |x-1| + |x-2 | + |x-3| + |x-4| remains constant when __________ \text{\_\_\_\_\_\_\_\_\_\_} .

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

1 ≤ x ≤ 4 1\leq x \leq 4 1 ≤ x ≤ 2 1\leq x \leq 2 2 ≤ x ≤ 3 2\leq x \leq 3 3 ≤ x ≤ 4 3\leq x \leq 4

Pi Han Goh by Pi Han Goh , 30, Malaysia

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1 solution

Bhavya Jain
Jul 20, 2016

When we make the graph we see it is constant and equal to 4 in the interval 2 to 3

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