|x + 1| ≤ 4 হলে, a এবং b এর কোন মানের জন্য a ≤ 3x - 2 ≤ b হবে?
Solution
Correct Answer: Option A
|x + 1| ≤ 4
⇒ - 4 ≤ x + 1 ≤ 4
⇒ - 4 - 1 ≤ x + 1 - 1 ≤ 4 - 1
⇒ - 5 ≤ x ≤ 3
⇒ - 15 ≤ 3x ≤ 9
⇒ - 15 - 2 ≤ 3x - 2 ≤ 9 - 2
⇒ - 17 ≤ 3x - 2 ≤ 7
যেখানে, a ≤ 3x - 2 ≤ b
∴ a = - 17 এবং b = 7
⇒ - 4 ≤ x + 1 ≤ 4
⇒ - 4 - 1 ≤ x + 1 - 1 ≤ 4 - 1
⇒ - 5 ≤ x ≤ 3
⇒ - 15 ≤ 3x ≤ 9
⇒ - 15 - 2 ≤ 3x - 2 ≤ 9 - 2
⇒ - 17 ≤ 3x - 2 ≤ 7
যেখানে, a ≤ 3x - 2 ≤ b
∴ a = - 17 এবং b = 7
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