Absolute Value Inequalities – MCQs

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

Question 1:

\[
\text{Solve the inequality: } |x – 3| < 5.
\]
\[
\text{(a) } -2 < x < 8, \quad \text{(b) } x < -2 \text{ or } x > 8, \quad \text{(c) } x \geq -2, \quad \text{(d) } x \leq 8
\]
Answer: A

Question 2:

\[
\text{Solve: } |2x + 1| \geq 7.
\]
\[
\text{(a) } x \leq -4 \text{ or } x \geq 3, \quad \text{(b) } -4 < x < 3, \quad \text{(c) } x > -4, \quad \text{(d) } x < 3
\]
Answer: A

Question 3:

\[
\text{Find the solution set for } |x + 5| > 9.
\]
\[
\text{(a) } x > 4 \text{ or } x < -14, \quad \text{(b) } x < 4 \text{ or } x > -14, \quad \text{(c) } x > 9 \text{ or } x < -4, \quad \text{(d) } x > 4 \text{ or } x < -14
\]
Answer: D

Question 4:

\[
\text{Solve: } |x – 7| \leq 2.
\]
\[
\text{(a) } 5 \leq x \leq 9, \quad \text{(b) } x \leq 5 \text{ or } x \geq 9, \quad \text{(c) } x > 5, \quad \text{(d) } x < 9
\]
Answer: A

Question 5:

\[
\text{What is the solution to } |3x – 2| < 4?
\]
\[
\text{(a) } -\frac{2}{3} < x < 2, \quad \text{(b) } x < -\frac{2}{3} \text{ or } x > 2, \quad \text{(c) } x > -\frac{2}{3}, \quad \text{(d) } x < 2
\]
Answer: A

Question 6:

\[
\text{Solve: } |x + 6| \geq 3.
\]
\[
\text{(a) } x \leq -9 \text{ or } x \geq -3, \quad \text{(b) } x < -9 \text{ or } x > -3, \quad \text{(c) } -9 < x < -3, \quad \text{(d) } x > -9
\]
Answer: A

Question 7:

\[
\text{Solve: } |4x – 1| < 7.
\]
\[
\text{(a) } -\frac{3}{2} < x < 2, \quad \text{(b) } x < -\frac{3}{2} \text{ or } x > 2, \quad \text{(c) } x > -\frac{3}{2}, \quad \text{(d) } x < 2
\]
Answer: A

Question 8:

\[
\text{Find the solution for } |5 – 2x| \geq 9.
\]
\[
\text{(a) } x \leq -2 \text{ or } x \geq 7, \quad \text{(b) } -2 < x < 7, \quad \text{(c) } x > -2, \quad \text{(d) } x < 7
\]
Answer: A

Question 9:

\[
\text{Solve: } |x| < 4.
\]
\[
\text{(a) } -4 < x < 4, \quad \text{(b) } x < -4 \text{ or } x > 4, \quad \text{(c) } x > -4, \quad \text{(d) } x < 4
\]
Answer: A

Question 10:

\[
\text{Find the solution to } |x – 2| \leq 5.
\]
\[
\text{(a) } -3 \leq x \leq 7, \quad \text{(b) } x < -3 \text{ or } x > 7, \quad \text{(c) } x > -3, \quad \text{(d) } x < 7
\]
Answer: A

Question 11:

\[
\text{Solve: } |x – 1| > 3.
\]
\[
\text{(a) } x < -2 \text{ or } x > 4, \quad \text{(b) } x > -2 \text{ and } x < 4, \quad \text{(c) } -2 \leq x \leq 4, \quad \text{(d) } x \geq -2 \text{ or } x \leq 4
\]
Answer: A

Question 12:

\[
\text{Find the solution for } |x + 4| \geq 7.
\]
\[
\text{(a) } x \leq -11 \text{ or } x \geq 3, \quad \text{(b) } -11 < x < 3, \quad \text{(c) } x > -11, \quad \text{(d) } x < 3
\]
Answer: A

Question 13:

\[
\text{Solve: } |3x + 2| < 5.
\]
\[
\text{(a) } -\frac{7}{3} < x < 1, \quad \text{(b) } x < -\frac{7}{3} \text{ or } x > 1, \quad \text{(c) } x > -\frac{7}{3}, \quad \text{(d) } x < 1
\]
Answer: A

Question 14:

\[
\text{Find the solution for } |x – 8| \leq 3.
\]
\[
\text{(a) } 5 \leq x \leq 11, \quad \text{(b) } x < 5 \text{ or } x > 11, \quad \text{(c) } x > 5, \quad \text{(d) } x < 11
\]
Answer: A

Question 15:

\[
\text{Solve: } |x + 1| > 6.
\]
\[
\text{(a) } x < -7 \text{ or } x > 5, \quad \text{(b) } x > -7 \text{ and } x < 5, \quad \text{(c) } -7 \leq x \leq 5, \quad \text{(d) } x \geq -7 \text{ or } x \leq 5
\]
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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