Inequalities – Algebra MCQs

By: Prof. Dr. Fazal Rehman Shamil | Last updated: January 31, 2025

Question 1:

\[
\text{Solve the inequality: } 3x – 5 > 7.
\]
\[
\text{(a) } x > 4, \quad \text{(b) } x > \frac{4}{3}, \quad \text{(c) } x > 3, \quad \text{(d) } x > \frac{5}{3}
\]
Answer: A

Question 2:

\[
\text{Which of the following is the solution set for } 2x + 4 \leq 10?
\]
\[
\text{(a) } x \leq 3, \quad \text{(b) } x \leq 2, \quad \text{(c) } x \geq 3, \quad \text{(d) } x \geq 2
\]
Answer: A

Question 3:

\[
\text{If } -4x + 7 < 3, \text{ then the solution for } x \text{ is:} \] \[ \text{(a) } x > 1, \quad \text{(b) } x < 1, \quad \text{(c) } x > -1, \quad \text{(d) } x < -1
\]
Answer: D

Question 4:

\[
\text{Solve: } 5x – 2 \geq 3x + 6.
\]
\[
\text{(a) } x \geq 4, \quad \text{(b) } x \geq 2, \quad \text{(c) } x \leq 4, \quad \text{(d) } x \leq 2
\]
Answer: A

Question 5:

\[
\text{Which inequality represents all numbers greater than -2 but less than 5?}
\]
\[
\text{(a) } -2 < x < 5, \quad \text{(b) } -2 \leq x \leq 5, \quad \text{(c) } x \leq -2 \text{ or } x \geq 5, \quad \text{(d) } x < -2 \text{ or } x > 5
\]
Answer: A

Question 6:

\[
\text{Solve: } 4 – 3(x + 1) > -2.
\]
\[
\text{(a) } x < \frac{10}{3}, \quad \text{(b) } x > -\frac{10}{3}, \quad \text{(c) } x > \frac{10}{3}, \quad \text{(d) } x < -\frac{10}{3}
\]
Answer: A

Question 7:

\[
\text{Solve for } x: \quad 6 – 2x \leq 10.
\]
\[
\text{(a) } x \geq -2, \quad \text{(b) } x \leq -2, \quad \text{(c) } x \geq 2, \quad \text{(d) } x \leq 2
\]
Answer: B

Question 8:

\[
\text{If } -3(x – 2) > 6, \text{ then } x \text{ is:}
\]
\[
\text{(a) } x < 0, \quad \text{(b) } x > 0, \quad \text{(c) } x < -4, \quad \text{(d) } x > -4
\]
Answer: D

Question 9:

\[
\text{Find the solution of } \frac{x}{3} – 4 \leq 2.
\]
\[
\text{(a) } x \leq 18, \quad \text{(b) } x \leq 12, \quad \text{(c) } x \geq 12, \quad \text{(d) } x \geq 18
\]
Answer: B

Question 10:

\[
\text{Which inequality represents the statement: “All real numbers greater than or equal to -5”?}
\]
\[
\text{(a) } x \leq -5, \quad \text{(b) } x > -5, \quad \text{(c) } x \geq -5, \quad \text{(d) } x < -5
\]
Answer: C

Question 11:

\[
\text{Solve: } 3(x – 1) < 2x + 5.
\]
\[
\text{(a) } x < 8, \quad \text{(b) } x > 8, \quad \text{(c) } x < -8, \quad \text{(d) } x > -8
\]
Answer: D

Question 12:

\[
\text{Solve the compound inequality: } -2 < 3x – 1 \leq 5.
\]
\[
\text{(a) } -\frac{1}{3} < x \leq 2, \quad \text{(b) } -\frac{1}{3} > x \geq 2, \quad \text{(c) } -\frac{1}{3} \leq x < 2, \quad \text{(d) } -\frac{1}{3} \geq x > 2
\]
Answer: A

Question 13:

\[
\text{Solve: } 4x – 7 > 2x + 5.
\]
\[
\text{(a) } x > 6, \quad \text{(b) } x > 5, \quad \text{(c) } x < 5, \quad \text{(d) } x < 6
\]
Answer: B

Question 14:

\[
\text{Find the solution set for } 2(x + 3) < 4x – 1. \] \[ \text{(a) } x > 7, \quad \text{(b) } x < 7, \quad \text{(c) } x > -7, \quad \text{(d) } x < -7
\]
Answer: B

Question 15:

\[
\text{Solve the inequality: } 5 – 2x > 3x – 4.
\]
\[
\text{(a) } x < 3, \quad \text{(b) } x > 3, \quad \text{(c) } x < -3, \quad \text{(d) } x > -3
\]
Answer: A

More MCQs on Algebra (Collected from Past Papers)

  1. Elementary Algebra – MCQs
  2. Algebraic Expressions – MCQs
  3. Algebraic Identities – MCQs
  4. Commutative Algebra – MCQs
  5. Linear Equations – MCQs
  6. Graphing Linear Equations – MCQs
  7. Inequalities in Algebra – MCQs
  8. Absolute Value Inequalities – MCQs
  9. Exponent – MCQs
  10. Exponential Functions – MCQs
  11. Logarithms – MCQs
  12. Polynomials – MCQs
  13. Factoring Methods – MCQs
  14. Polynomial Arithmetic – MCQs
  15. Quadratic Equation – MCQs
  16. Linear Algebra – MCQs
  17. Matrices in Algebra – MCQs
  18. Functions in Algebra – MCQs
  19. Sequences in Algebra – MCQs
  20. Arithmetic in Algebra – MCQs
  21. Combining Like Terms in Algebra – MCQs
  22. Abstract Algebra – MCQs
  23. Sets in Algebra – MCQs
  24. Algebra Calculator – MCQs

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