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Absolute Value Function

If |x-3|+|x-2...

Question

If $| x - 3 | + | x - 2 | = 1$ , then $x \in$

A

[2, 3]

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B

(2, 3]

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C

[2, 3)

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D

(2, 3)

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Solution

The correct option is A $[2, 3]$
$| x - 3 | + | x - 2 | = 1$
When $x < 2$
$- 2 x + 5 = 1$
$\Rightarrow x = 2$ No solution

When $2 \leq x < 3$
$1 = 1$ which is true

When $x \geq 3$
$2 x - 5 = 1$
$\Rightarrow x = 3$

$∴ x \in [2, 3]$

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Absolute Value Function

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