1.9.1 Rearranging an Equation in Three Variables

Algebra 11.9.1 Rearranging an Equation in Three Variables

Search for key terms or text.

Warm Up

In an earlier lesson, you saw the equation $V + F - 2 = E$ , which relates the number of vertices, faces, and edges in a Platonic solid.

In questions 1 - 2, write an equation that makes it easier to find the number of vertices in each of the Platonic solids described:

An octahedron (shown here), which has 8 faces

A line drawing of an octahedron, a geometric shape with eight triangular faces. Solid lines show visible edges, and dotted lines represent hidden edges, illustrating its three-dimensional structure.

Compare your answer: $V = E - 6$

$V + 8 - 2 = E$

$V + 6 = E$

$V = E - 6$

An icosahedron, which has 30 edges

Compare your answer: $V = 32 - F$

$V + F - 2 = 30$

$V + F - 2 + 2 = 30 + 2$

$V + F = 32$

$F = 32 - F$

A Buckminsterfullerene (also called a “Buckyball”) is a polyhedron with 60 vertices. It is not a Platonic solid, but the numbers of faces, edges, and vertices are related the same way as those in a Platonic solid.

Write an equation that makes it easier to find the number of faces a Buckyball has if we know how many edges it has.

Compare your answer: $F = E - 58$

$V + F - 2 = E$

$60 + F - 2 = E$

$58 + F = E$

$58 - 58 + F = E - 58$

$F = E - 58$

Why Should I Care?

Illustration of a woman holding a piggy bank, surrounded by icons representing savings goals such as a car, house, calendar, credit card, calculator, airplane, graph, and documents with money symbols.

Alex's brother can use algebra to budget his paycheck from his job at a pizza place. He uses some money for food, some for going out with his friends, and some, he saves for college.

If he uses variables to represent the different ways he uses his money, he can put those variables into an equation to make sure he has enough money to last until his next paycheck.

Previous Next

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

Use the information below to generate a citation. We recommend using a citation tool such as this one.
- Authors: Lynn Marecek, MaryAnne Anthony-Smith, Andrea Honeycutt Mathis, Jay Abramson, Sharon North, Amy Baldwin, Alyssa Howell
- Publisher/website: OpenStax
- Book title: Algebra 1
- Publication date: Jun 4, 2025
- Location: Houston, Texas
- Book URL: https://openstax.org/books/algebra-1/pages/about-this-course
- Section URL: https://openstax.org/books/algebra-1/pages/1-9-1-rearranging-an-equation-in-three-variables

© 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.