The set of all values of x satisfying the inequations $|x -1|≤5$ and $|x|≥2$, is
Answer & explanation
Correct answer: option 3
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 $x∈(-∞,-2]∪[2, ∞)$
$⇒ x∈[-4, -2] ∪ [2, 6]$