Lesson 3: Absolute Values of Rational Numbers — Practice Questions

1. 1. Solve the equation: $|y| = -3$.

   • A. $y = 3$
   • B. $y = -3$
   • C. $y = 3$ or $y = -3$
   • D. No solution

2. 2. Solve the inequality $|2x + 3| + 5 < 4$. Write the solution in interval notation. If no solution exists, enter 'none'. The solution is ___.

3. 3. What is the solution to the inequality $|7x + 2| + 8 < 4$?

   • A. No solution
   • B. All real numbers
   • C. $x < -\frac{6}{7}$
   • D. $x > \frac{2}{7}$

4. 4. Solve the equation $\dfrac{1}{2}|x + 5| + 4 = 1$. If there is no solution, enter "none". The solution is ___.

5. 5. Solve the equation $\dfrac{3}{2}|x - 2| + 5 = 2$. If there is no solution, enter "none". The solution is ___.

6. 6. Solve the equation $|4x + 3| + 3 = 1$. If there is no solution, enter "none". The solution is ___.

7. 7. Solve the inequality $|x - 4| \leq -1$. Write the solution in interval notation. If no solution exists, enter 'none'. The solution is ___.

8. 8. What is the solution set for the inequality $|x - 5| > -2$?

   • A. All real numbers
   • B. No solution
   • C. $x > 7$
   • D. $x < 3$

9. 9. What is the solution to the inequality $5|x| + 6 \geq 1$?

   • A. All real numbers
   • B. No solution
   • C. $x \geq 1$ or $x \leq -1$
   • D. $[-1, 1]$

10. 10. Solve the equation: $|x| = 4$.

    • A. $x = 4$ or $x = -4$
    • B. $x = 4$
    • C. $x = -4$
    • D. No solution