The value(s) of $x$ for which the expression $y = | x + 2 | + | x - 7 |$ is minimum is/are

- 4

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5

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9

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Solution

The correct option is C $5$
$y = | x + 2 | + | x - 7 |$
Here, the turning points are $- 2, 7$
$y = ⎧ ⎨ ⎩ \begin{matrix} - (x + 2) - (x - 7), & x < - 2 (x + 2) - (x - 7), & - 2 \leq x < 7 (x + 2) + (x - 7), & x \geq 7 \end{matrix} \Rightarrow y = ⎧ ⎨ ⎩ \begin{matrix} 5 - 2 x, & x < - 2 9, & - 2 \leq x < 7 2 x - 5, & x \geq 7 \end{matrix}$

Graph will be

$y$ will be minimum for any value of $x \in [- 2, 7]$

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