Solve the inequality 5x - 7 ≥ 3x + 9.

• A. x ≥ 8
• B. x ≤ 8
• C. x ≥ 16
• D. x ≤ -8

Answer: (A)

Solving a linear inequality by isolating x shows when one side is at least as large as the other. Start with 5x - 7 ≥ 3x + 9. Subtract 3x from both sides to get 2x - 7 ≥ 9. Then add 7 to both sides to obtain 2x ≥ 16. Divide by the positive 2 to get x ≥ 8. The boundary value 8 is included because the inequality is “greater than or equal to.” At x = 8, both sides equal 33, so the inequality holds exactly there, and for any x larger than 8 it continues to hold since the left side grows faster than the right. The solution set is x with x ≥ 8.