If 3-x- 5- then which of the following can be true-

Given that nbsp; 3≤|x|≤ 5 From the properties of the Modulus Function, nbsp; If a≤|x|≤ b, where a,b gt;0 then b≤ x≤ a nbsp;or a≤ x≤ b ⇒ x∈ [ b, a]∪[a, ...

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If 3≤|x|≤ 5, ...

Question

If $3 \leq | x | \leq 5$ , then which of the following can be true?

x \in [- 3, 3]

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x \in (- 3, 3)

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None of these

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x \in [- 5, - 3] \cup [3, 5]

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Solution

The correct option is D $x \in [- 5, - 3] \cup [3, 5]$
Given that $3 \leq | x | \leq 5$

From the properties of the Modulus Function,
If $a \leq | x | \leq b$ , where $a, b > 0$ then
$- b \leq x \leq - a$ or $a \leq x \leq b$
$\Rightarrow x \in [- b, - a] \cup [a, b]$

Here we have $3 \leq | x | \leq 5 \Rightarrow x \in [- 5, - 3] \cup [3, 5]$

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If 3≤|x|≤5, then which of the following can be true?

The correct option is D x∈[−5,−3]∪[3,5] Given that 3≤|x|≤5 From the properties of the Modulus Function, If a≤|x|≤b, where a,b>0 then −b≤x≤−a or a≤x≤b ⇒x∈[−b,−a]∪[a,b] Here we have 3≤|x|≤5⇒x∈[−5,−3]∪[3,5]

If $3 \leq | x | \leq 5$ , then which of the following can be true?