Lesson 3: Inequalities — Practice Questions

1. 1. A club is fundraising and needs to raise at least 800 dollars. They have already collected 550 dollars. What is the minimum amount of money, $m$, they still need to raise? $m \geq$ ___

2. 2. A delivery truck has a maximum weight capacity of 4000 pounds. It is already carrying 2100 pounds of packages. Which inequality represents the additional weight, $w$, that can be added?

   • A. $2100 + w \geq 4000$
   • B. $2100 + w \leq 4000$
   • C. $w - 2100 \leq 4000$
   • D. $4000 - w > 2100$

3. 3. You have a gift card with a balance of 90 dollars. After buying an item that costs $c$ dollars, you want the remaining balance to be at least 15 dollars. What is the most the item can cost? $c \leq$ ___

4. 4. Which situation is best modeled by the inequality $x + 25 \geq 70$?

   • A. A fish tank can hold at most 70 gallons and already has 25 gallons in it.
   • B. You need a score of at least 70 on a test and have 25 points so far.
   • C. You have 70 dollars and spend 25 dollars on a gift.
   • D. A bookshelf holds 70 books and currently has 25 books on it.

5. 5. A player has 200 health points. After taking $d$ points of damage from a trap, their health must remain above 50 to avoid being defeated. Solve for the possible values of $d$. $d <$ ___

6. 6. Is $x=6$ a solution to the inequality $4x - 9 < 15$?

   • A. Yes
   • B. No

7. 7. When checking if $y = -3$ is a solution to the inequality $5y + 8 \leq -5$, what is the value of the expression on the left side? ___

8. 8. Which of the following values for $a$ is a solution to the inequality $8a + 3 \geq 7$?

   • A. $a = 0$
   • B. $a = \frac{1}{4}$
   • C. $a = \frac{1}{2}$
   • D. $a = -1$

9. 9. Is $z = 4$ a solution to the inequality $20 - 3z > 8$?

   • A. Yes
   • B. No

10. 10. To check if $p=10$ is a solution for $6p - 5 > 4p + 12$, the left side simplifies to 55. What does the right side simplify to? ___