One-variable equations and inequalities Knowledge-Based Practice

Questions

1. 1.

   What is the solution set of the inequality $|2x - 7| > 5$?

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

   What is the solution set of the compound inequality $2x - 3 \le 3x + 2 < 2x + 8$?

   • A) $(-5, 6]$
   • B) $[-5, 6]$
   • C) $[-5, 6)$
   • D) $(-5, 6)$
3. 3.

   Given that $x$ is a real number satisfying $-3 < x \le 4$, what is the sum of all integer values that the expression $5 - 2x$ can take?

   • A) 18
   • B) 52
   • C) 49
   • D) 60
4. 4.

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

   • A) $\{-11\}$
   • B) $\{5\}$
   • C) $\{1\}$
   • D) $\{-4\}$
5. 5.

   What is the sum of all real solutions to the equation $|x - 2| + |2x - 4| = 9$?

   • A) 2
   • B) 4
   • C) 6
   • D) 8
6. 6.

   For what real value of $m$ does the equation $4(mx - 2) = 12x - 3m + 1$ have infinitely many real solutions?

   • A) -3
   • B) 3
   • C) 1
   • D) -1
7. 7.

   What is the solution set of the equation $|2x - 3| = x + 6$?

   • A) $\{-9, 1\}$
   • B) $\{9\}$
   • C) $\{-3, 9\}$
   • D) $\{-1, 9\}$
8. 8.

   How many integer values of $x$ satisfy the inequality $|3x - 7| \le 14$?

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

   What is the solution set of the inequality $-7 \le \frac{3 - 2x}{5} < 1$?

   • A) $(-1, 19]$
   • B) $[-1, 19)$
   • C) $(-19, 1]$
   • D) $[-19, 1)$
10. 10.

    What is the solution set of the inequality $5(x - 2) - 8x \le 2(x + 7) - 4$?

    • A) $x \le -4$
    • B) $x \ge 4$
    • C) $x \ge -4$
    • D) $x \le 4$

Answers and step-by-step solutions appear after you finish the test.