Solve the inequality 4x + 3 > 2x - 5.

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

Answer: (B)

Solving a linear inequality uses the same algebraic moves as solving an equation, with the rule that you keep the inequality sign in the same direction when you add or subtract or divide by a positive number. Start with 4x + 3 > 2x − 5. Subtract 2x from both sides to collect the x terms: 2x + 3 > −5. Then subtract 3 from both sides: 2x > −8. Divide by the positive 2: x > −4. So every number greater than −4 makes the inequality true, meaning the solution set is all x with x > −4 (that is, values to the right of −4 on the number line). You can check a sample value, like x = −3.9: the left side is −12.6 and the right side is −12.8, and indeed −12.6 > −12.8. At x = −4 the sides are equal, which does not satisfy the strict inequality, and any smaller x fails as well.