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Inequalities Involving Modulus Function

If ||x|-5|x+5...

Question

If $∣ ∣ | x | - 5 ∣ ∣ (x + 5) < 0$ , then $x \in$

A

(- \infty, - 5)

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B

(- \infty, 5)

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C

[0, 5]

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D

(0, 5)

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Solution

The correct option is A $(- \infty, - 5)$
$∣ ∣ | x | - 5 ∣ ∣ (x + 5) < 0$
$\Rightarrow x + 5 < 0 (∵ | | x | - 5 | \geq 0)$
$\Rightarrow x < - 5 ∴ x \in (- \infty, - 5)$

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Inequalities Involving Modulus Function

Standard XII Mathematics

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