Solve For \[$ Y \$\] In The Equation:$\[ \frac{y}{8} = -8 \\]Possible Solutions:A. 0 B. \[$-16\$\] C. 64 D. \[$-64\$\]

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Introduction

In mathematics, solving for a variable in an equation is a fundamental concept that is essential for understanding various mathematical operations and relationships. In this article, we will focus on solving for y in the equation y8=−8\frac{y}{8} = -8. We will break down the solution process into simple steps, making it easy to understand and follow.

Understanding the Equation

The given equation is y8=−8\frac{y}{8} = -8. To solve for y, we need to isolate y on one side of the equation. The equation involves a fraction, where y is the numerator and 8 is the denominator.

Step 1: Multiply Both Sides by 8

To isolate y, we need to get rid of the fraction. We can do this by multiplying both sides of the equation by 8. This will cancel out the denominator on the left side of the equation.

y8×8=−8×8\frac{y}{8} \times 8 = -8 \times 8

This simplifies to:

y=−64y = -64

Step 2: Check the Solution

Now that we have solved for y, we need to check if the solution is correct. We can do this by plugging the solution back into the original equation.

−648=−8\frac{-64}{8} = -8

This simplifies to:

−8=−8-8 = -8

Since the equation holds true, we can confirm that the solution is correct.

Conclusion

In this article, we solved for y in the equation y8=−8\frac{y}{8} = -8. We broke down the solution process into simple steps, making it easy to understand and follow. We multiplied both sides of the equation by 8 to isolate y, and then checked the solution by plugging it back into the original equation. The correct solution is y = -64.

Possible Solutions

Based on the solution process, we can identify the possible solutions as follows:

  • A. 0: This is not a possible solution, as the equation does not equal 0.
  • B. -16: This is not a possible solution, as the equation does not equal -16.
  • C. 64: This is not a possible solution, as the equation does not equal 64.
  • D. -64: This is the correct solution, as the equation equals -64.

Final Answer

The final answer is −64\boxed{-64}.

Additional Tips and Resources

If you are struggling to solve for y in an equation, here are some additional tips and resources that may help:

  • Make sure to follow the order of operations (PEMDAS) when solving equations.
  • Use algebraic properties, such as the distributive property and the commutative property, to simplify equations.
  • Check your solution by plugging it back into the original equation.
  • Practice solving equations with different variables and coefficients to build your skills and confidence.

References

Discussion

Introduction

In our previous article, we solved for y in the equation y8=−8\frac{y}{8} = -8. We broke down the solution process into simple steps, making it easy to understand and follow. In this article, we will answer some frequently asked questions (FAQs) about solving for y in the equation.

Q&A

Q: What is the first step in solving for y in the equation y8=−8\frac{y}{8} = -8?

A: The first step is to multiply both sides of the equation by 8 to get rid of the fraction.

Q: Why do we multiply both sides of the equation by 8?

A: We multiply both sides of the equation by 8 to cancel out the denominator on the left side of the equation, which is 8.

Q: What is the next step after multiplying both sides of the equation by 8?

A: After multiplying both sides of the equation by 8, we simplify the equation to get y = -64.

Q: How do we check if the solution is correct?

A: We check if the solution is correct by plugging it back into the original equation. If the equation holds true, then the solution is correct.

Q: What are some common mistakes to avoid when solving for y in the equation y8=−8\frac{y}{8} = -8?

A: Some common mistakes to avoid when solving for y in the equation y8=−8\frac{y}{8} = -8 include:

  • Not multiplying both sides of the equation by 8
  • Not simplifying the equation after multiplying both sides by 8
  • Not checking the solution by plugging it back into the original equation

Q: What are some additional tips for solving for y in the equation y8=−8\frac{y}{8} = -8?

A: Some additional tips for solving for y in the equation y8=−8\frac{y}{8} = -8 include:

  • Make sure to follow the order of operations (PEMDAS) when solving equations
  • Use algebraic properties, such as the distributive property and the commutative property, to simplify equations
  • Check your solution by plugging it back into the original equation
  • Practice solving equations with different variables and coefficients to build your skills and confidence

Q: What are some real-world applications of solving for y in the equation y8=−8\frac{y}{8} = -8?

A: Some real-world applications of solving for y in the equation y8=−8\frac{y}{8} = -8 include:

  • Calculating the cost of goods sold in a business
  • Determining the amount of money owed on a loan
  • Finding the area of a rectangle or square

Conclusion

In this article, we answered some frequently asked questions (FAQs) about solving for y in the equation y8=−8\frac{y}{8} = -8. We covered topics such as the first step in solving for y, why we multiply both sides of the equation by 8, and how to check if the solution is correct. We also provided some additional tips and real-world applications of solving for y in the equation.

Final Answer

The final answer is −64\boxed{-64}.

Additional Resources

Discussion

Do you have any questions or comments about solving for y in the equation y8=−8\frac{y}{8} = -8? Share your thoughts and feedback in the discussion section below!