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# help

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If |x - y| = 4, |y - z| = 5, and |z - w| = 7, what is the smallest possible value of |x - w|?

Jun 13, 2020

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That means $$\begin{cases}x - y = \pm4 \\y - z = \pm5 \\ z - w = \pm7\end{cases}$$

Let $$a = x-y, b = y- z, c = z- w$$

$$x - w = a + b + c$$

We can interpret the question as finding the minimum sum over a, b and c.

By trying all 8 possible combinations, we get the smallest possible value to be |4 + 5 + (-7)| = 2

Jun 13, 2020