Table of Contents |
In mathematics, we work with equivalent equations all the time. Think about the process for solving a multi-step equation. We might start with something such as . Using inverse operations, we create a series of equivalent equations in order to find a value for x.
Subtract 3 from both sides | |
This is considered an equivalent equation. Divide both sides by 4 to get another equivalent equation. | |
A second equivalent equation |
The equations above are all considered equivalent equations, because they have the same solution. In each equation, the solution is
In order to determine if two equations are equivalent, we will solve each equation, and then compare their solutions. If their solutions are the same, we can say the equations are equivalent. If the solutions are not the same, we know that the equations are not equivalent.
EXAMPLE
Determine if the equations below are equivalent:Subtract 2 from both sides | |
Divide both sides by -5 | |
Our Solution |
Subtract 14 from both sides | |
Divide both sides by -4 | |
Our Solution |
EXAMPLE
Determine if the equations below are equivalent:Subtract 2 from both sides | |
Divide both sides by -3 | |
Our Solution |
Subtract 9 from both sides | |
Multiply both sides by 2 | |
Our Solution |
Source: ADAPTED FROM "BEGINNING AND INTERMEDIATE ALGEBRA" BY TYLER WALLACE, AN OPEN SOURCE TEXTBOOK AVAILABLE AT www.wallace.ccfaculty.org/book/book.html. License: Creative Commons Attribution 3.0 Unported License