Inequality Word Problems worksheet - Free Printable

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

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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, the price $ x $ must satisfy:
$$
x \leq 4
$$

✔ Answer: C. $ x \leq 4 $

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

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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, height $ x $ satisfies:
$$
x \geq 4
$$

✔ Answer: D. $ x \geq 4 $

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

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

- "More than 90" means her average score is above 90, but not 90.
- So, $ x > 90 $

✔ Answer: B. $ x > 90 $

> ✔ Explanation: "More than" means strictly greater than — does not include 90.

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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 $ x $ must be at least 500 meters.
- So, $ x \geq 500 $

✔ Answer: $ x \geq 500 $

> ✔ Explanation: "Or higher" includes 500 and everything above it.

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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:
- You can spend $10 or less → $ x \leq 10 $
- Also, $ 10 \geq x $ is the same as $ x \leq 10 $

Now check the options:

- $ x \leq 10 $ → ✔ Correct
- $ x > 10 $ → ✘ (you cannot spend more than $10)
- $ 10 \geq x $ → ✔ Same as $ x \leq 10 $, so correct
- $ 10 < x $ → ✘ (means spending more than $10, which is not allowed)

✔ Circle:
- $ x \leq 10 $
- $ 10 \geq x $

> ✔ Explanation: Both expressions mean "the amount spent is no more than $10".

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✔ 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 as a printable answer sheet!