Skip to ContentGo to accessibility pageKeyboard shortcuts menu
OpenStax Logo
Algebra 1

2.8.3 Writing Inequalities to Represent Constraints

Algebra 12.8.3 Writing Inequalities to Represent Constraints

Search for key terms or text.

Activity

An elevator car in a skyscraper can hold at most 15 people. For safety reasons, each car can carry a maximum of 1,500 kg. On average, an adult weighs 70 kg and a child weighs 35 kg. Assume that each person carries 4 kg of gear with them.

1.

Write as many equations and inequalities as you can think of to represent the constraints in this situation. Be sure to specify the meaning of any letters that you use. (Avoid using the letters zz, mm, or gg.)

2.

After you have finished the following tasks, explain the adjustments you made to the equations and inequalities so that they are communicated more clearly.

Trade your work with a partner and read each other’s equations and inequalities.

  • Explain to your partner what you think their statements mean, and listen to their explanation of yours.
  • Make adjustments to your equations and inequalities so that they are communicated more clearly.
3.

Rewrite your equations and inequalities so that they would work for a different building where:

  • an elevator car can hold at most zz people
  • each car can carry a maximum of mm kilograms
  • each person carries dd kg of gear

Video: Writing Inequalities to Represent Constraints Solution 

Watch the following video to further explain the solution to the activity you just completed.

Self Check

Serena is running a juice shop. Oranges cost $2 per pound. She can spend at most $64 per day on oranges. If pp represents the number of pounds of oranges Serena can buy per day, which of the following inequalities is true?

Additional Resources

Applications with Linear Inequalities

Many real-life situations require us to solve inequalities. The method we will use to solve applications with linear inequalities is very much like the one we used when we solved applications with equations.

We will read the problem and make sure all the words are understood. Next, we will identify what we are looking for and assign a variable to represent it. We will restate the problem in one sentence to make it easy to translate into an inequality.

Example 

Dawn won a mini-grant of $4,000 to buy tablet computers for her classroom. The tablets she would like to buy cost $254.12 each, including tax and delivery. Write an inequality to represent the maximum number of tablets Dawn can buy.

Solution

Step 1 - Read the problem.

Step 2 - Identify what you are looking for. the maximum number of tablets Dawn can buy

Step 3 - Name what you are looking for.

Choose a variable to represent that quantity. Let n=n= the number of tablets.

Step 4 - Translate. Write a sentence that gives the information to find it.

$254.12 times the number of tablets is no more than $4,000. Translate into an inequality. 254.12n4000254.12n4000

Try it

Try It: Applications with Linear Inequalities

1.

Angie has $20 to spend on juice boxes for her son’s preschool picnic. Each pack of juice boxes costs $2.63. Write an inequality to represent the maximum number of packs, pp, she can buy.

2.

Daniel wants to surprise his girlfriend with a birthday party at her favorite restaurant. It will cost $42.75 per person for dinner, including tip and tax. His budget for the party is $500. Write an inequality to represent the maximum number of people, nn, Daniel can have at the party.

Citation/Attribution

This book may not be used in the training of large language models or otherwise be ingested into large language models or generative AI offerings without OpenStax's permission.

Want to cite, share, or modify this book? This book uses the Creative Commons Attribution-NonCommercial-ShareAlike License and you must attribute OpenStax.

Attribution information
  • If you are redistributing all or part of this book in a print format, then you must include on every physical page the following attribution:

    Access for free at https://openstax.org/books/algebra-1/pages/about-this-course

  • If you are redistributing all or part of this book in a digital format, then you must include on every digital page view the following attribution:

    Access for free at https://openstax.org/books/algebra-1/pages/about-this-course

Citation information

© May 21, 2025 OpenStax. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike License . The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.