Solve the inequality 3t - 7 > 11.

Solve the inequality 3t - 7 > 11.

• A. t > 6
• B. t < 6
• C. t >= 6
• D. t > 5

Answer: (A)

Solving linear inequalities means undoing the operations around t while keeping the inequality sign in the correct direction. Start with 3t - 7 > 11. Add 7 to both sides to move the constant: 3t > 18. Divide both sides by 3 (a positive number), so the inequality direction stays the same: t > 6. This means every number greater than 6 makes the left side exceed 11. For example, if t = 7, then 3(7) - 7 = 14, which is greater than 11. If t = 6, the left side is 11, which is not greater than 11, so 6 doesn’t work. Therefore, the correct description is t is greater than 6. The other options don’t match this exact threshold.

Solving linear inequalities means undoing the operations around t while keeping the inequality sign in the correct direction. Start with 3t - 7 > 11. Add 7 to both sides to move the constant: 3t > 18. Divide both sides by 3 (a positive number), so the inequality direction stays the same: t > 6. This means every number greater than 6 makes the left side exceed 11. For example, if t = 7, then 3(7) - 7 = 14, which is greater than 11. If t = 6, the left side is 11, which is not greater than 11, so 6 doesn’t work. Therefore, the correct description is t is greater than 6. The other options don’t match this exact threshold.