Inequality Word Problems worksheet - Free Printable

Let's solve each of these inequality word problems step by step and explain the reasoning.

---

1. The price of a 2-pack Shopkin should not be more than $4. Choose an inequality for this situation.

- "Should not be more than $4" means the price can be $4 or less.
- So, if $ x $ is the price, then:
$$
x \leq 4
$$

✔ Answer: C. $ x \leq 4 $

> ✔ Explanation: "Not more than" means less than or equal to.

---

2. The height of a person should not be less than 4 ft to ride the roller coaster. Choose an inequality for this situation.

- "Should not be less than 4 ft" means the height must be 4 ft or more.
- So, if $ x $ is the height, then:
$$
x \geq 4
$$

✔ Answer: D. $ x \geq 4 $

> ✔ Explanation: "Not less than" means greater than or equal to.

---

3. Ashley scores more than 90 A on an average in all subjects. Choose an inequality to represent this situation.

- "More than 90" means greater than 90, not including 90.
- So, if $ x $ is her average score:
$$
x > 90
$$

✔ Answer: B. $ x > 90 $

> ✔ Explanation: "More than" means strictly greater than, so we use $ > $, not $ \geq $.

---

4. Aimee is flying a plane for the first time! The air traffic controller tells her to fly at 500 m above the ground or higher. Write an inequality that is true only for elevations at which Aimee should fly.

- "500 m or higher" means elevation is at least 500 meters.
- Let $ x $ = elevation in meters.
- Then:
$$
x \geq 500
$$

✔ Answer: $ x \geq 500 $

> ✔ Explanation: "Or higher" includes 500, so we use $ \geq $.

---

5. I have $10 to spend at Claire’s. Circle the inequalities that explain this situation.

- You have $10 to spend, meaning you can spend up to $10, but not more.
- So, if $ x $ is the amount spent:
$$
x \leq 10
$$
Also, since $ 10 \geq x $ is the same as $ x \leq 10 $, both are equivalent.

Now let's check each option:

- $ x \leq 10 $ → ✔ Correct (you can spend up to $10)
- $ x > 10 $ → ✘ Incorrect (can't spend more than $10)
- $ 10 \geq x $ → ✔ Same as $ x \leq 10 $, so correct
- $ 10 < x $ → ✘ Means spending more than $10, not allowed

✔ Correct answers to circle:
- $ x \leq 10 $
- $ 10 \geq x $

> ✔ Explanation: Both express that spending cannot exceed $10.

---

✔ Final Answers:

1. C. $ x \leq 4 $
2. D. $ x \geq 4 $
3. B. $ x > 90 $
4. $ x \geq 500 $
5. Circle: $ x \leq 10 $ and $ 10 \geq x $

Let me know if you'd like this formatted for printing or explained further!