If $| x - 1 | + | x - 4 | = 4$ , then $x \in$

{- \frac{1}{2}, \frac{9}{2}}

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{\frac{1}{2}, \frac{9}{2}}

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{- \frac{9}{2}, \frac{1}{2}}

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{- \frac{9}{2}, - \frac{1}{2}}

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Solution

The correct option is B ${\frac{1}{2}, \frac{9}{2}}$
If $x < 1$ ,
$- x + 1 - x + 4 = 4$
$\Rightarrow x = \frac{1}{2}$

If $1 \leq x < 4$ ,
$x - 1 - x + 4 = 4$
$\Rightarrow 3 = 4$ (Not possible)

If $x \geq 4$ ,
$x - 1 + x - 4 = 4$
$\Rightarrow x = \frac{9}{2}$

$∴ x = \frac{1}{2}, \frac{9}{2}$

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