Lesson 6: Compound Inequalities — Practice Questions

1. 1. An athlete's daily calorie intake, `c`, should be at least 2200 and no more than 2800. Which inequality represents this recommended range?

   • A. $c < 2200$ or $c > 2800$
   • B. $2200 \leq c \leq 2800$
   • C. $2200 < c < 2800$
   • D. $c \leq 2200$ or $c \geq 2800$

2. 2. To ride a roller coaster, a person's height, `h` in inches, must be at least 48 but no more than 72. Write a compound inequality for the acceptable height range. ___

3. 3. A store offers a discount on items priced less than 15 dollars or more than 200 dollars. Which inequality represents a price, `p`, that gets a discount?

   • A. $15 \leq p \leq 200$
   • B. $p < 15$ or $p > 200$
   • C. $p \leq 15$ or $p \geq 200$
   • D. $15 < p < 200$

4. 4. A manufactured part is rejected if its length, `L` in mm, is shorter than 45 or longer than 55. Write a compound inequality for the length of a rejected part. ___

5. 5. The pH level, `p`, of a swimming pool should be between 7.2 and 7.6, inclusive. Write a compound inequality to represent this acceptable range. ___

6. 6. Solve the chain inequality $-3 < 3x - 6 < 9$. The solution is ___.

7. 7. Which value of $x$ is in the solution set of both $2x + 1 > 5$ and $x - 4 \leq 3$?

   • A. $x = 1$
   • B. $x = 3$
   • C. $x = 5$
   • D. $x = 8$

8. 8. Solve the chain inequality $-4 < -2x + 2 < 8$. Written from least to greatest, the solution is ___.

9. 9. When solving a chain inequality and dividing all three parts by a negative number, what must happen to the inequality symbols?

   • A. They stay the same
   • B. Only the left symbol flips
   • C. All inequality symbols flip
   • D. The middle expression becomes zero

10. 10. What is the solution set of the 'and' compound inequality: $3x - 2 \leq 10$ and $x + 1 > -2$?

    • A. $-3 < x \leq 4$
    • B. $x \leq 4$
    • C. $x > -3$
    • D. $-3 \leq x < 4$