In the realm of mathematical expressions, the equivalence of two expressions is a fundamental concept that empowers us to simplify complex equations and unlock their underlying relationships. This exploration delves into the intriguing question of which expression is equivalent to 0.5y+10.5+6.5y-0.5-0.5y,
guiding us through a journey of simplification and identification.
As we embark on this intellectual adventure, we will uncover the intricacies of algebraic operations, the significance of equivalent expressions, and the practical applications of this knowledge in problem-solving.
Simplifying the Expression
The given expression is 0.5y+10.5+6.5y-0.5-0.5y. To simplify this expression, we can combine like terms.
First, we can combine the terms with y: 0.5y+6.5y-0.5y = 6y.
Next, we can combine the constants: 10.5-0.5 = 10.
Therefore, the simplified expression is 6y+10.
Identifying Equivalent Expressions: Which Expression Is Equivalent To 0.5y+10.5+6.5y-0.5-0.5y
An equivalent expression is an expression that has the same value as another expression for all values of the variables.
The expression 6y+10 is equivalent to the expression 0.5y+10.5+6.5y-0.5-0.5y because both expressions simplify to 6y+10.
Creating a Table for Comparison
| Given Expression | Equivalent Expression |
|---|---|
| 0.5y+10.5+6.5y-0.5-0.5y | 6y+10 |
Illustrating the Simplification
The flowchart shows the steps involved in simplifying the given expression.
Elaborating on the Equivalence
The equivalence between the two expressions is significant because it means that we can use either expression to solve a mathematical problem.
For example, if we are solving the equation 0.5y+10.5+6.5y-0.5-0.5y = 15, we can use either the given expression or the equivalent expression 6y+10 to solve for y.
Key Questions Answered
What is the significance of equivalent expressions?
Equivalent expressions are essential because they allow us to represent the same mathematical value in different forms. This flexibility is invaluable in problem-solving, as it enables us to manipulate expressions in ways that simplify calculations and reveal hidden relationships.
How can we apply the concept of equivalent expressions in real-world scenarios?
The concept of equivalent expressions finds applications in various fields, including finance, physics, and engineering. For instance, in finance, equivalent expressions are used to simplify complex interest rate calculations, while in physics, they are employed to derive equations that describe physical phenomena.
