Solve 2x + 3 ≤ x + 7.

• A. x ≥ 4
• B. x < 4
• C. x > 4
• D. x ≤ 4

Answer: (D)

The key idea is solving a linear inequality by applying the same operations on both sides while the direction of the inequality stays the same (you only flip if you multiply or divide by a negative number).

Start by removing x from the right side: subtract x from both sides to get x + 3 ≤ 7. Then remove the constant by subtracting 3 from both sides: x ≤ 4. Since the relation is ≤, the boundary value is included, so x can be 4 or any number smaller than 4.

Quick check: plug in x = 4 → both sides are 11, so it works. If x > 4, the left side becomes larger than the right, which breaks the inequality. If x < 4, the inequality holds.