Algebra 1 quiz: solving 'and' compound inequalities

📚 Quick Study Guide

• 🔢 An 'and' compound inequality combines two inequalities with the word 'and'. It represents the intersection of the two inequalities.
• 🧭 To solve an 'and' compound inequality, solve each inequality separately.
• 📈 The solution to an 'and' compound inequality includes all values that satisfy both inequalities.
• ✍️ Graph the solution by finding the overlapping region of the two individual inequality graphs on a number line.
• 🧮 The solution can be written in the form $a \le x \le b$ or as an intersection of two sets.
• 💡 When solving, remember to perform the same operation on all parts of the inequality to isolate the variable.

🧪 Practice Quiz

1. What is the solution to the compound inequality $2 < x + 1 \le 5$?
   1. $1 < x \le 4$
   2. $1 \le x < 4$
   3. $3 < x \le 6$
   4. $3 \le x < 6$
2. Which of the following represents the graph of $-3 \le x < 2$?
   1. A closed circle at -3, shading to the left, and an open circle at 2, shading to the right.
   2. A closed circle at -3, shading to the right, and an open circle at 2, shading to the left.
   3. An open circle at -3, shading to the right, and a closed circle at 2, shading to the left.
   4. An open circle at -3, shading to the left, and a closed circle at 2, shading to the right.
3. Solve the compound inequality $-1 < 2x - 5 < 3$:
   1. $2 < x < 4$
   2. $3 < x < 4$
   3. $2 \le x \le 4$
   4. $3 \le x \le 4$
4. What values of $x$ satisfy both $x + 3 > 5$ and $x - 2 < 1$?
   1. $2 < x < 3$
   2. $x > 2$ or $x < 3$
   3. $x > 8$ and $x < 3$
   4. No solution
5. Which inequality is equivalent to $4 \le x - 1 < 7$?
   1. $3 \le x < 6$
   2. $5 \le x < 8$
   3. $5 < x \le 8$
   4. $3 < x \le 6$
6. Find the solution set for the compound inequality $1 \le 3x + 4 \le 10$:
   1. $-1 \le x \le 2$
   2. $-1 < x < 2$
   3. $-5/3 \le x \le 2$
   4. $-5/3 < x < 2$
7. Which of the following represents the interval notation of the solution to $0 \le 2x + 2 < 6$?
   1. $[-1, 2)$
   2. $(-1, 2]$
   3. $[-1, 4)$
   4. $(-1, 4]$