Writing Equivalent EquationsWhich Equations Could You Use To Find The Price Of One Tire Patch? Select All That Apply.To Prepare For His Mountain Biking Trip, Rhyan Bought Four Tire Patches. Rhyan Paid Using A Gift Card That Had $x$ Dollars

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Introduction

In mathematics, equivalent equations are expressions that have the same solution set. They are often used to represent different forms of the same equation, making it easier to solve and manipulate. In this article, we will explore the concept of equivalent equations and provide examples of how they can be used to find the price of one tire patch.

What are Equivalent Equations?

Equivalent equations are expressions that have the same solution set. They are often used to represent different forms of the same equation, making it easier to solve and manipulate. For example, the equations 2x = 6 and x = 3 are equivalent because they have the same solution set, which is x = 3.

Types of Equivalent Equations

There are several types of equivalent equations, including:

  • Multiplication and Division Equations: These equations involve multiplying or dividing both sides of the equation by the same non-zero number.
  • Addition and Subtraction Equations: These equations involve adding or subtracting the same value from both sides of the equation.
  • Rearrangement Equations: These equations involve rearranging the terms of the equation to make it easier to solve.

Example: Finding the Price of One Tire Patch

Let's say Rhyan bought four tire patches for a total of $x dollars. We want to find the price of one tire patch. We can use equivalent equations to represent this situation.

Step 1: Write an Equation

Let's say the price of one tire patch is y dollars. We can write an equation to represent this situation:

4y = x

This equation states that the total cost of four tire patches is equal to the total amount of money Rhyan paid, which is x dollars.

Step 2: Solve for y

To find the price of one tire patch, we need to solve for y. We can do this by dividing both sides of the equation by 4:

y = x/4

This equation states that the price of one tire patch is equal to the total amount of money Rhyan paid divided by 4.

Step 3: Write an Equivalent Equation

We can write an equivalent equation to represent the situation:

y = x/4

This equation is equivalent to the original equation because it has the same solution set.

Conclusion

In this article, we explored the concept of equivalent equations and provided examples of how they can be used to find the price of one tire patch. We saw that equivalent equations can be used to represent different forms of the same equation, making it easier to solve and manipulate. We also saw that equivalent equations can be used to find the price of one tire patch by dividing the total amount of money paid by the number of tire patches.

Key Takeaways

  • Equivalent equations are expressions that have the same solution set.
  • There are several types of equivalent equations, including multiplication and division equations, addition and subtraction equations, and rearrangement equations.
  • Equivalent equations can be used to represent different forms of the same equation, making it easier to solve and manipulate.
  • Equivalent equations can be used to find the price of one tire patch by dividing the total amount of money paid by the number of tire patches.

Frequently Asked Questions

  • What is an equivalent equation? An equivalent equation is an expression that has the same solution set as another equation.
  • How can equivalent equations be used to find the price of one tire patch? Equivalent equations can be used to find the price of one tire patch by dividing the total amount of money paid by the number of tire patches.
  • What are some examples of equivalent equations? Examples of equivalent equations include multiplication and division equations, addition and subtraction equations, and rearrangement equations.

References

Additional Resources

Q&A: Writing Equivalent Equations

Q: What is an equivalent equation?

A: An equivalent equation is an expression that has the same solution set as another equation. In other words, if two equations have the same solution set, they are equivalent.

Q: How can equivalent equations be used to find the price of one tire patch?

A: Equivalent equations can be used to find the price of one tire patch by dividing the total amount of money paid by the number of tire patches. For example, if Rhyan paid $x dollars for four tire patches, we can write an equation to represent this situation:

4y = x

We can then solve for y by dividing both sides of the equation by 4:

y = x/4

This equation states that the price of one tire patch is equal to the total amount of money Rhyan paid divided by 4.

Q: What are some examples of equivalent equations?

A: Examples of equivalent equations include:

  • Multiplication and Division Equations: These equations involve multiplying or dividing both sides of the equation by the same non-zero number. For example, the equations 2x = 6 and x = 3 are equivalent because they have the same solution set, which is x = 3.
  • Addition and Subtraction Equations: These equations involve adding or subtracting the same value from both sides of the equation. For example, the equations x + 2 = 5 and x = 3 are equivalent because they have the same solution set, which is x = 3.
  • Rearrangement Equations: These equations involve rearranging the terms of the equation to make it easier to solve. For example, the equations x + 2 = 5 and 2 + x = 5 are equivalent because they have the same solution set, which is x = 3.

Q: How can I determine if two equations are equivalent?

A: To determine if two equations are equivalent, you can use the following steps:

  1. Check if the equations have the same solution set: If the equations have the same solution set, they are equivalent.
  2. Check if the equations can be transformed into each other: If the equations can be transformed into each other by multiplying or dividing both sides by the same non-zero number, adding or subtracting the same value from both sides, or rearranging the terms, they are equivalent.

Q: What are some real-world applications of equivalent equations?

A: Equivalent equations have many real-world applications, including:

  • Finance: Equivalent equations can be used to calculate interest rates, investment returns, and other financial metrics.
  • Science: Equivalent equations can be used to model physical systems, such as the motion of objects, the behavior of electrical circuits, and the flow of fluids.
  • Engineering: Equivalent equations can be used to design and optimize systems, such as bridges, buildings, and electronic circuits.

Q: How can I practice writing equivalent equations?

A: To practice writing equivalent equations, you can try the following exercises:

  • Write equivalent equations for simple algebraic expressions: For example, write equivalent equations for the expression 2x + 3.
  • Write equivalent equations for more complex algebraic expressions: For example, write equivalent equations for the expression x^2 + 4x + 4.
  • Solve equivalent equations: For example, solve the equation 2x + 3 = 5.

Conclusion

In this article, we explored the concept of equivalent equations and provided examples of how they can be used to find the price of one tire patch. We also answered some frequently asked questions about equivalent equations and provided some real-world applications of equivalent equations. We hope that this article has been helpful in understanding the concept of equivalent equations and how they can be used in a variety of contexts.