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Inequalities Involving Modulus Function

If -4≤|x|≤2, ...

Question

If $- 4 \leq | x | \leq 2$ , then $x$ belongs to

A

[- 4, 2]

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B

[2, 4]

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C

[- 4, 4]

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D

[- 2, 2]

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Solution

The correct option is D $[- 2, 2]$
$- 4 \leq | x | \leq 2$
Since $| x | \geq 0$ (always)
$∴ - 4 \leq | x | \leq 2 \Rightarrow | x | \leq 2$
$\Rightarrow - 2 \leq x \leq 2$

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