Concept explainers
Writing Describe the difference between an equation that is defined as an identity and an equation that has no solution. Provide an example of each and explain why each example is an identity or has no solution.
To find: The difference between an equation which has many solutions and has no solution. Provide example and explain.
Answer to Problem 33P
If both sides of the equation are same when we solve the equation then it is identity(has many solutions). If both sides of the equation are not then it has no solution.
Explanation of Solution
Given information: An equation that is defined as an identity and an equation that has no solution.
When solve the equation both sides gives same number or variable then it is identity equation.
For example,
5x+10=5(x+2)
Distribute the right side
5x+10=5x+10
Subtract both sides 5x
10=10
Now, when tried to solve for x both sides of the equation are same numbers. It means it has infinitely many solutions and it is called equation that is defined as an identity.
Example for no solution equation:
5x+10=5(x+1)
Distribute to get rid the parentheses,
5x+10 =5x+5
Subtract both sides 5x.
10=5
Now, both sides of the equation are NOT same numbers. So, there is NO solution to the equation.
Chapter 2 Solutions
High School Math 2012 Common-core Algebra 1 Practice And Problem Solvingworkbook Grade 8/9
Additional Math Textbook Solutions
Elementary Algebra: Concepts and Applications (10th Edition)
Elementary Algebra
Algebra and Trigonometry (6th Edition)
Linear Algebra and Its Applications (5th Edition)
College Algebra in Context with Applications for the Managerial, Life, and Social Sciences (5th Edition)
- Algebra and Trigonometry (6th Edition)AlgebraISBN:9780134463216Author:Robert F. BlitzerPublisher:PEARSONContemporary Abstract AlgebraAlgebraISBN:9781305657960Author:Joseph GallianPublisher:Cengage LearningLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
- Algebra And Trigonometry (11th Edition)AlgebraISBN:9780135163078Author:Michael SullivanPublisher:PEARSONIntroduction to Linear Algebra, Fifth EditionAlgebraISBN:9780980232776Author:Gilbert StrangPublisher:Wellesley-Cambridge PressCollege Algebra (Collegiate Math)AlgebraISBN:9780077836344Author:Julie Miller, Donna GerkenPublisher:McGraw-Hill Education