Solve -1-x-2- 1- x- 2

−1|x|−2≥ 1 ⇒ nbsp; 1 +1|x|−2≤ 0 ⇒|x|−1|x|−2≤ 0 ⇒ |x| − 1≤ 0 and |x| − 2 gt; 0 ⇒ |x|≤ 1 and |x| gt; 2 Not possible Or, |x| − 1≥ 0 and |x| − 2 lt; 0 ⇒ ...

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Byju's Answer

Standard XIII

Mathematics

Inequalities Involving Modulus Function

Solve −1|x|−2...

Question

Solve $\frac{- 1}{| x | - 2} \geq 1, x \neq \pm 2$

[1, 2)

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(- 2, - 1] \cup [1, 2)

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[- 1, 1]

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(- 2, - 1]

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Solution

The correct option is B $(- 2, - 1] \cup [1, 2)$
$\frac{- 1}{| x | - 2} \geq 1 \Rightarrow 1 + \frac{1}{| x | - 2} \leq 0 \Rightarrow \frac{| x | - 1}{| x | - 2} \leq 0$
$\Rightarrow | x | - 1 \leq 0$ and $| x | - 2 > 0$
$\Rightarrow | x | \leq 1$ and $| x | > 2$ Not possible

Or, $| x | - 1 \geq 0$ and $| x | - 2 < 0$
$\Rightarrow | x | \geq 1$ and $| x | < 2$
$\Rightarrow x \in (- \infty, - 1] \cup [1, \infty) and x \in (- 2, 2)$

$∴ x \in (- 2, - 1] \cup [1, 2)$

Suggest Corrections

Solve −1|x|−2≥1, x≠±2

The correct option is B (−2,−1]∪[1,2) −1|x|−2≥1⇒1+1|x|−2≤0⇒|x|−1|x|−2≤0 ⇒|x|−1≤0 and |x|−2>0 ⇒|x|≤1 and |x|>2 Not possible Or, |x|−1≥0 and |x|−2<0 ⇒|x|≥1 and |x|<2 ⇒x∈(−∞,−1]∪[1,∞) and x∈(−2,2) ∴x∈(−2,−1]∪[1,2)

Solve $\frac{- 1}{| x | - 2} \geq 1, x \neq \pm 2$