Solve the inequality: 2x - 5 < 9

• A. x < -2
• B. x > 7
• C. x < 7
• D. x ≤ 7

Answer: (C)

When solving a linear inequality, you isolate x just like in an equation, but you keep the inequality sign the same (since you’re not multiplying or dividing by a negative number here). Start with 2x - 5 < 9. Add 5 to both sides to get 2x < 14. Divide by 2 (a positive number), giving x < 7. This means any number less than 7 makes the left-hand side smaller than 9. The boundary is at x = 7, which is not included because the inequality is strict. Quick checks: x = 0 gives -5 < 9 (true); x = 6.9 gives 2(6.9) - 5 = 8.8 < 9 (true); x = 7 gives 9 < 9 (false); x = 8 gives 11 < 9 (false). So the solution is all x with x < 7.