Solve -3x + 7 > 1

• A. x ≥ 2
• B. x ≤ 2
• C. x > 2
• D. x < 2

Answer: (D)

Start from -3x + 7 > 1. Subtract 7 from both sides to isolate the term with x: -3x > -6. When you divide by -3, the inequality flips because you’re dividing by a negative number, so x < 2. Since the inequality is strict, 2 itself doesn’t work (plugging in x = 2 makes the left side equal to 1, which is not greater than 1). The left-hand side decreases as x increases, so values smaller than 2 keep -3x + 7 above 1. For example, x = 0 gives 7 > 1, while x = 3 gives -2 > 1 false. Therefore, all real numbers less than 2 satisfy the inequality.