Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 6 - Algebra: Equations and Inequalities - 6.2 Linear Equations in One Variable and Proportions - Concept and Vocabulary Check - Page 362: 11


In solving an equation with variable x, if you eliminate the variable and obtain a statement such as\[6=6\], the equation is true for every value of x. The solution set can be expressed in set builder notation as, \[\left\{ x|x\text{ is a real number} \right\}\].

Work Step by Step

While solving an equation if the variable on both the sides of an equation gets eliminated and still left-hand side equals the right-hand side, then the equation is correct or true for every value of x, because no matter what value x takes, the equation is satisfied by its own. The representation for the same is given as\[\left\{ x|x\text{ is a real number} \right\}\]. This means for every real value of x, it will satisfy the equation.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.