Misc 6 - Solve 7 <= (3x + 1) / 2 <= 11 - Chapter 6 Class 11 - Miscellaneous

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Misc 6 Solve the inequality 7 ≤ (3𝑥 + 11)﷮2﷯ ≤ 11 7 ≤ (3𝑥 + 11)﷮2﷯ ≤ 11 Multiplying 2 all sides(Eliminating 2) 7 × 2 ≤ (3x + 11) ≤ 11 × 2 14 ≤ 3x + 11 ≤ 22 Subtracting 11 all sides(Eliminating 11) 14 – 11 ≤ 3x – 11 ≤ 22 – 11 3 ≤ 3x ≤ 11 Dividing 3 all sides(Eliminating 3) 3﷮3﷯ ≤ 3𝑥﷮3﷯ ≤ 11﷮3﷯ 1 ≤ x ≤ 11﷮3﷯ Thus, x is a real number which is less than or equal to 11﷮3﷯ and greater than or equal to 1 Hence, x ∈ 𝟏, 𝟏𝟏﷮𝟑﷯﷯ is the solution

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