The set of all values of x satisfying th

CUET Preparation Today

Start Free Mocks

Home Questions 823JVZURJ3

Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Relations and Functions

Question:

The set of all values of x satisfying the inequations $|x -1|≤5$ and $|x|≥2$, is

Options:

[-4, 6]

[-4, -2]

[-4, -2] ∪ [2, 6]

[2, 6]

Correct Answer:

[-4, -2] ∪ [2, 6]

Explanation:

The correct answer is Option 3: [-4, -2] ∪ [2, 6]

We have,

$|x -1|≤5$ and $|x|≥2$

$⇒-5≤x-1≤5$ and $(x≤-2\,or\,x≥2)$

$⇒-4≤x≤6$ and $(x≤-2\,or\,x≥2)$

$⇒ x∈[-4, 6]$ and $x∈(-∞,-2]∪[2, ∞)$

$⇒ x∈[-4, -2] ∪ [2, 6]$