The set of all real x satisfying the inequality 4 − ∣ x ∣ 3 − ∣ x ∣ ≥ 0 , is

Given, 4 − ∣ x ∣ 3 − ∣ x ∣ ≥ 0 ⇒ 3 − ∣ x ∣ ≤ 0 and 4 − ∣ x ∣ 4 or ∣ x ∣ ≤ 3 and ∣ x ∣ 4 or ∣ x ∣ ≤ 3 ⇒ x ∈ ( − ∞ , − 4 ) ∪ [ − 3 , 3 ] ∪ ( 4 , ∞ )

Mathematics - Quadratic Equation Question with Solution | TestHub

MathematicsQuadratic EquationInequationMedium2 minPYQ_2013

MathematicsMediumsingle choice

The set of all real $x$ satisfying the inequality $\frac{3 - ∣ x ∣}{4 - ∣ x ∣} \geq 0,$ is

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Solution:

Given, $\frac{3 - ∣ x ∣}{4 - ∣ x ∣} \geq 0$ $\Rightarrow 3 - ∣ x ∣ \leq 0$ and $4 - ∣ x ∣ < 0$ or $3 - ∣ x ∣ \geq 0$ and $4 - ∣ x ∣ < 0$ $\Rightarrow ∣ x ∣ \geq 3$ and $∣ x ∣ > 4$ or $∣ x ∣ \leq 3$ and $∣ x ∣ < 4$ $\Rightarrow ∣ x ∣ > 4$ or $∣ x ∣ \leq 3$ $\Rightarrow x \in (- \infty, - 4) \cup [- 3, 3] \cup (4, \infty)$

Stream:JEESubject:MathematicsTopic:Quadratic EquationSubtopic:Inequation

⏱ 2mℹ️ Source: PYQ_2013

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