Question

Solve the inequalities : [x - 1] ≤ 5, [x] ≥ 2​

Answer 1

Answer:

|x – 1| ≤ 5 and |x| ≥ 2

⇒ -5 ≤ x – 1 ≤ 5 and x ≤ -2 (or) x > 2

⇒ – 5 + 1 ≤ x ≤ 5 + 1

⇒ -4 ≤ x ≤ 6 and x ≤ -2 (or) x ≥ 2

Hence x < [-4, -2] ∪ [2, 6]

Answer 2

Step-by-step explanation:

|x – 1| ≤ 5 and |x| ≥ 2

⇒ -5 ≤ x – 1 ≤ 5 and x ≤ -2 (or) x > 2

⇒ – 5 + 1 ≤ x ≤ 5 + 1

⇒ -4 ≤ x ≤ 6 and x ≤ -2 (or) x ≥ 2

Hence x < [-4, -2] ∪ [2, 6]

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