Inequality Word Problems Worksheet

Tackling inequality word problems can feel like navigating a maze, but with the right strategies and practice, they become much less daunting! Many students find themselves scratching their heads when faced with translating real-world scenarios into mathematical inequalities. The key is to carefully identify the key phrases that indicate inequality (greater than, less than, at least, at most) and then translate those phrases into the appropriate mathematical symbols. This process not only helps you solve the problem but also strengthens your understanding of how math applies to everyday situations.

This worksheet is designed to give you ample practice in setting up and solving these types of problems. From determining the minimum number of items needed to reach a sales goal to calculating the maximum amount of time you can spend on a task, these problems cover a wide range of applications. The goal isn’t just to find the “right” answer but to develop a systematic approach to problem-solving that you can apply to any inequality word problem you encounter.

Remember, the first step is always to define your variable. What are you trying to find? Once you’ve identified that, read the problem carefully and look for the keywords that signal an inequality. For example, “at least” means greater than or equal to (≥), while “less than” means strictly less than (<). "At most" translates to less than or equal to (≤), and "more than" signifies strictly greater than (>). Paying close attention to these details will ensure you translate the word problem into the correct mathematical inequality.

Once you have your inequality set up, solving it is usually straightforward. Just remember the golden rule: when you multiply or divide both sides of an inequality by a negative number, you must flip the inequality sign. This is a crucial step that’s easy to forget, but it can completely change the solution. After you’ve solved the inequality, it’s important to interpret your answer in the context of the original word problem. Does your solution make sense? Can you explain what it means in plain language?

This worksheet provides you with the opportunity to put these strategies into practice. By working through these problems, you’ll build your confidence and develop the skills necessary to conquer any inequality word problem that comes your way. Don’t be afraid to make mistakes – they’re a valuable part of the learning process. Review your work, identify where you went wrong, and learn from your errors. With consistent effort and a positive attitude, you’ll become a master of inequality word problems in no time!

Inequality Word Problems Worksheet Answers

Answers

Here are the answers to the Inequality Word Problems Worksheet. Please note that the exact wording of your solution may vary slightly depending on how you set up the inequality, but the underlying mathematical principles should be the same.

Problem 1: Let ‘x’ be the number of hours worked. The inequality is 10x ≥ 200. Solution: x ≥ 20. Answer: At least 20 hours must be worked.
Problem 2: Let ‘c’ be the number of cookies. The inequality is 2c + 3 ≤ 15. Solution: c ≤ 6. Answer: At most 6 cookies can be purchased.
Problem 3: Let ‘s’ be the score on the test. The inequality is (80 + 90 + s)/3 ≥ 85. Solution: s ≥ 85. Answer: The score must be at least 85.
Problem 4: Let ‘n’ be the number of notebooks. The inequality is 2n + 5 < 15. Solution: n < 5. Answer: Fewer than 5 notebooks can be purchased.
Problem 5: Let ‘p’ be the price of the pants. The inequality is p + 25 ≤ 60. Solution: p ≤ 35. Answer: The pants can cost at most $35.
Problem 6: Let ‘t’ be the time spent running. The inequality is 5 + t ≤ 30. Solution: t ≤ 25. Answer: You can spend at most 25 minutes running.
Problem 7: Let ‘m’ be the number of members. The inequality is 10m > 150. Solution: m > 15. Answer: More than 15 members are needed.
Problem 8: Let ‘w’ be the weight of the package. The inequality is w ≤ 50. Solution: w ≤ 50. Answer: The package can weigh at most 50 pounds.
Problem 9: Let ‘r’ be the number of rides. The inequality is 2r + 5 ≤ 20. Solution: r ≤ 7.5. Since you can’t ride half a ride, the answer is 7. Answer: You can go on at most 7 rides.
Problem 10: Let ‘d’ be the amount donated. The inequality is d ≥ 100. Solution: d ≥ 100. Answer: You must donate at least $100.

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