One-variable equations and inequalities Knowledge-Based Download PDF

Questions

1. 1.

   What is the solution set of the inequality $|x - 5| < |x + 1|$?

   • A) $(-\infty, 2)$
   • B) $(-\infty, 5)$
   • C) $(2, \infty)$
   • D) $(5, \infty)$
2. 2.

   What is the solution set of the system of inequalities $2x - 5 < 5x + 4$ and $3(x - 1) \ge 5x - 11$?

   • A) (-3, 4)
   • B) [-3, 4]
   • C) (-3, 4]
   • D) [-3, 4)
3. 3.

   What is the solution set of the inequality $1 < |2x - 5| \le 7$?

   • A) $[-1, 2) \cup (3, 6]$
   • B) $(-1, 2] \cup [3, 6)$
   • C) $[-6, -3) \cup (2, 5]$
   • D) $[-1, 6]$
4. 4.

   What is the solution set of the inequality $\frac{6}{|2x - 1|} \ge 3$?

   • A) $[-\frac{1}{2}, \frac{3}{2}]$
   • B) $[-\frac{1}{2}, \frac{3}{2}] \setminus \{\frac{1}{2}\}$
   • C) $(-\frac{1}{2}, \frac{3}{2})$
   • D) $(-\infty, -\frac{1}{2}] \cup [\frac{3}{2}, \infty)$
5. 5.

   How many distinct real solutions does the equation $| |2x - 1| - 5 | = 3$ have?

   • A) 1
   • B) 2
   • C) 3
   • D) 4
6. 6.

   What is the solution set of the equation $|3x - 1| = |x + 7|$?

   • A) $\left\{-4, \frac{3}{2}\right\}$
   • B) $\{4\}$
   • C) $\left\{-\frac{3}{2}, -4\right\}$
   • D) $\left\{-\frac{3}{2}, 4\right\}$
7. 7.

   What is the solution set of the equation $|2x - 5| = 3x + 1$?

   • A) $\left\{-6, \frac{4}{5}\right\}$
   • B) $\left\{\frac{4}{5}\right\}$
   • C) $\{-6\}$
   • D) $\emptyset$
8. 8.

   For which value of the constant a does the equation $a(x - 2) + 3x = 5(x + 1) - 4$ have no solution?

   • A) $a = -2$
   • B) $a = 2$
   • C) $a = -\frac{1}{2}$
   • D) $a = 5$
9. 9.

   How many integer values of $x$ satisfy the inequality $|2x - 3| \le 9$?

   • A) 8
   • B) 9
   • C) 10
   • D) 11
10. 10.

    What is the solution set of the inequality $-3 \le \frac{1 - 2x}{5} < 3$?

    • A) $[-8, 7)$
    • B) $(-7, 8)$
    • C) $[-7, 8)$
    • D) $(-7, 8]$
11. 11.

    What is the solution to the equation $\frac{2x - 3}{4} - \frac{x - 1}{3} = 1$?

    • A) 3
    • B) 7
    • C) $\frac{17}{2}$
    • D) $\frac{25}{2}$
12. 12.

    What is the solution set of the inequality $5 - 3(x - 2) > 2(x + 8)$?

    • A) $x < -1$
    • B) $x > -1$
    • C) $x < 1$
    • D) $x > 1$