Algebra 1 test questions on 'or' compound inequalities

📚 Quick Study Guide

🔍 Definition: A compound inequality with "or" means that at least one of the inequalities must be true for the compound inequality to be true. 💡 Solving: Solve each inequality separately. 📝 Graphing: The solution set includes all values that satisfy either inequality. On a number line, this is represented by shading the regions that satisfy each individual inequality. 🧮 Interval Notation: Express the solution set using interval notation, combining intervals where necessary. If the intervals do not connect, use the union symbol $\cup$. ➕ Example: Solve and graph $x < 2$ or $x > 5$.
• Solution: The solution includes all numbers less than 2 or greater than 5.
• Interval Notation: $(-\infty, 2) \cup (5, \infty)$

Practice Quiz

1. What is the solution to the compound inequality $x < -3$ or $x > 1$?
   1. $(-3, 1)$
   2. $(-\infty, -3) \cup (1, \infty)$
   3. $(-3, \infty)$
   4. $(-\infty, 1)$
2. Which of the following represents the graph of $x \leq 0$ or $x > 4$?
   1. A number line shaded between 0 and 4.
   2. A number line shaded to the left of 0 (including 0) and to the right of 4 (excluding 4).
   3. A number line shaded to the left of 0 (excluding 0) and to the right of 4 (including 4).
   4. A number line shaded to the right of 0 and to the left of 4.
3. Solve: $2x + 1 < 5$ or $3x - 2 > 10$
   1. $(-\infty, 2) \cup (4, \infty)$
   2. $(2, 4)$
   3. $(-\infty, 2)$
   4. $(4, \infty)$
4. Which compound inequality represents all numbers less than -1 or greater than or equal to 3?
   1. $x < -1$ or $x > 3$
   2. $x \leq -1$ or $x \geq 3$
   3. $x < -1$ or $x \geq 3$
   4. $x \leq -1$ or $x > 3$
5. What is the solution set for $-x > 2$ or $x - 5 > -2$?
   1. $(-5, -2)$
   2. $(-\infty, -2) \cup (3, \infty)$
   3. $(-\infty, -3) \cup (-2, \infty)$
   4. $(-\infty, -2) \cup (7, \infty)$
6. Solve the compound inequality: $4x - 3 \leq 5$ or $-2x < -6$
   1. $(-\infty, 2] \cup (3, \infty)$
   2. $(2, 3)$
   3. $(-\infty, 2) \cup [3, \infty)$
   4. $(-\infty, 2]$
7. Which of the following inequalities has NO SOLUTION?
   1. x > 5 or x < 10
   2. x < 5 or x > 5
   3. x < 5 or x < 3
   4. x > 5 or x > 10