Two-Step Inequality Word Problems Worksheet With Answers
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Two-step inequalities are fundamental components of algebra that help in solving various real-world problems. Understanding how to translate word problems into mathematical expressions is a crucial skill for students. In this article, we’ll explore the importance of two-step inequalities and provide a variety of word problems, along with a worksheet and answers for practice. 📚✨
What is a Two-Step Inequality?
A two-step inequality is an inequality that requires two operations to solve. It can take various forms, such as:
- Addition or subtraction followed by multiplication or division.
- Multiplication or division followed by addition or subtraction.
For example, the inequality ( 2x + 3 < 7 ) can be solved through two steps: first subtracting 3 from both sides and then dividing by 2.
Why Are Two-Step Inequalities Important?
Two-step inequalities are not only relevant in mathematics but also in practical applications. Students often encounter situations involving budgets, distance, and time constraints where inequalities can be helpful. Learning how to solve these inequalities prepares students for more advanced concepts in mathematics and helps in their daily decision-making.
Sample Two-Step Inequality Word Problems
Here, we present several word problems that require setting up and solving two-step inequalities.
Problem 1: Budgeting for a Party 🎉
Jessica is planning a party and has a budget of $200. She wants to buy snacks and drinks. Snacks cost $3 per person and drinks cost $2 per person. If she invites ( x ) people, how many people can she invite without exceeding her budget?
Inequality Setup: [ 3x + 2x \leq 200 ]
Problem 2: Speed Limit 🚗
A driver is traveling at a speed of ( x ) miles per hour. The speed limit on the road is 55 miles per hour. What speed should the driver maintain to be within the speed limit?
Inequality Setup: [ x < 55 ]
Problem 3: Distance Traveled 🚶♀️
Sarah walks at a speed of 3 miles per hour. She wants to walk for less than 2 hours. What is the maximum distance she can walk?
Inequality Setup: [ 3x < 6 ]
Problem 4: Concert Tickets 🎶
A concert has tickets priced at $45. A group of friends wants to buy tickets for ( x ) people but has only $300 to spend. How many people can they afford to take to the concert?
Inequality Setup: [ 45x \leq 300 ]
Worksheet for Practice
Below is a worksheet for students to practice solving two-step inequalities from the provided word problems.
Two-Step Inequality Worksheet
| Problem Number | Word Problem | Inequality Setup |
|---|---|---|
| 1 | Jessica is budgeting for a party. | ( 5x + 3 < 200 ) |
| 2 | A driver must maintain a speed below the limit of 70 mph. | ( x < 70 ) |
| 3 | Mike can walk 4 miles in less than 1 hour. How far can he walk? | ( 4x < 4 ) |
| 4 | The school is organizing a trip with a budget of $500 for field trips. | ( 100x \leq 500 ) |
Answers to the Worksheet
Here are the answers to the worksheet problems.
Answers
-
Problem 1:
- Inequality: ( 5x + 3 < 200 )
- Solution:
- Subtract 3: ( 5x < 197 )
- Divide by 5: ( x < 39.4 )
-
Problem 2:
- Inequality: ( x < 70 )
- Solution: No calculation needed.
-
Problem 3:
- Inequality: ( 4x < 4 )
- Solution:
- Divide by 4: ( x < 1 )
-
Problem 4:
- Inequality: ( 100x \leq 500 )
- Solution:
- Divide by 100: ( x \leq 5 )
Conclusion
Two-step inequalities provide a structured way to approach and solve real-world problems through algebra. With practice, students can develop the ability to translate complex situations into manageable equations. The worksheet provided can help reinforce these skills while offering an opportunity to apply what has been learned. Remember, practicing these problems consistently will enhance your understanding and proficiency in solving inequalities. Keep challenging yourself and enjoy the process of learning! 🧠💪