The value of x for which $| x - 2 | + | x - 8 | = 10$ is

3, 7

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2, 8

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1, 9

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0, 10

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Solution

The correct option is D
0, 10

Given: $| x - 2 | + | x - 8 | = 10$

$\Rightarrow$ $x - 2 + x - 8 = \pm 10$

Case 1

$x - 2 + x - 8 = 10$

$2 x - 10 = 10$

$2 x = 20$

$\Rightarrow$ $x = 10$

Case 2

$x - 2 + x - 8 = - 10$

$2 x - 10 = - 10$

$2 x = 0$

$\Rightarrow$ $x = 0$

Hence, $x$ can take the values 10,0

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| x - 2 | + | x - 8 | = 10

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