Solve The Equation: 3 − Y − 9 = 7 \frac{3}{-y} - 9 = 7 − Y 3 ​ − 9 = 7

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Introduction

Solving equations is a fundamental concept in mathematics, and it requires a deep understanding of algebraic operations and techniques. In this article, we will focus on solving a specific equation, $\frac{3}{-y} - 9 = 7$, which involves fractions and variables. We will break down the solution step by step, using clear explanations and examples to help readers understand the process.

Understanding the Equation

The given equation is $\frac{3}{-y} - 9 = 7$. To solve this equation, we need to isolate the variable $y$. The equation involves a fraction, which can be challenging to work with. However, with the right techniques and strategies, we can simplify the equation and solve for $y$.

Step 1: Add 9 to Both Sides

The first step in solving the equation is to add 9 to both sides of the equation. This will help us eliminate the negative term and simplify the equation.

$\frac{3}{-y} - 9 + 9 = 7 + 9$

Simplifying the equation, we get:

$\frac{3}{-y} = 16$

Step 2: Multiply Both Sides by $-y$

To eliminate the fraction, we need to multiply both sides of the equation by $-y$. This will help us get rid of the denominator and simplify the equation.

$-y \times \frac{3}{-y} = 16 \times -y$

Simplifying the equation, we get:

$3 = -16y$

Step 3: Divide Both Sides by $-16$

The final step in solving the equation is to divide both sides of the equation by $-16$. This will help us isolate the variable $y$ and find its value.

$\frac{3}{-16} = y$

Simplifying the equation, we get:

$y = -\frac{3}{16}$

Conclusion

Solving the equation $\frac{3}{-y} - 9 = 7$ requires a step-by-step approach and a deep understanding of algebraic operations and techniques. By adding 9 to both sides, multiplying both sides by $-y$, and dividing both sides by $-16$, we can simplify the equation and solve for $y$. The final solution is $y = -\frac{3}{16}$.

Tips and Tricks

• When working with fractions, it's essential to simplify the equation by eliminating the denominator.
• Multiplying both sides of the equation by a variable can help eliminate the fraction.
• Dividing both sides of the equation by a constant can help isolate the variable.

Real-World Applications

Solving equations is a fundamental concept in mathematics, and it has numerous real-world applications. In physics, equations are used to describe the motion of objects, while in engineering, equations are used to design and optimize systems. In finance, equations are used to model and analyze financial data.

Common Mistakes

• Failing to simplify the equation by eliminating the denominator.
• Multiplying both sides of the equation by a variable without considering the implications.
• Dividing both sides of the equation by a constant without considering the implications.

Conclusion

Solving the equation $\frac{3}{-y} - 9 = 7$ requires a deep understanding of algebraic operations and techniques. By following the step-by-step approach outlined in this article, readers can simplify the equation and solve for $y$. The final solution is $y = -\frac{3}{16}$.

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Introduction

In our previous article, we solved the equation $\frac{3}{-y} - 9 = 7$ step by step. However, we understand that readers may have questions and doubts about the solution. In this article, we will address some of the most frequently asked questions about solving the equation.

Q: What is the first step in solving the equation?

A: The first step in solving the equation is to add 9 to both sides of the equation. This will help us eliminate the negative term and simplify the equation.

Q: Why do we multiply both sides of the equation by $-y$?

A: We multiply both sides of the equation by $-y$ to eliminate the fraction. This is a common technique used to simplify equations involving fractions.

Q: What is the final solution to the equation?

A: The final solution to the equation is $y = -\frac{3}{16}$.

Q: Can you explain the concept of isolating the variable?

A: Isolating the variable means getting the variable by itself on one side of the equation. In this case, we want to isolate the variable $y$ by getting rid of the fraction and the constant term.

Q: What are some common mistakes to avoid when solving equations?

A: Some common mistakes to avoid when solving equations include:

• Failing to simplify the equation by eliminating the denominator.
• Multiplying both sides of the equation by a variable without considering the implications.
• Dividing both sides of the equation by a constant without considering the implications.

Q: How do you know when to add or subtract a term from both sides of the equation?

A: You know when to add or subtract a term from both sides of the equation when you want to eliminate a term or simplify the equation. For example, in this case, we added 9 to both sides of the equation to eliminate the negative term.

Q: Can you explain the concept of equivalent equations?

A: Equivalent equations are equations that have the same solution. In this case, the equation $\frac{3}{-y} - 9 = 7$ is equivalent to the equation $3 = -16y$.

Q: How do you know when to multiply or divide both sides of the equation by a variable or constant?

A: You know when to multiply or divide both sides of the equation by a variable or constant when you want to eliminate a fraction or simplify the equation. For example, in this case, we multiplied both sides of the equation by $-y$ to eliminate the fraction.

Conclusion

Solving the equation $\frac{3}{-y} - 9 = 7$ requires a deep understanding of algebraic operations and techniques. By following the step-by-step approach outlined in this article, readers can simplify the equation and solve for $y$. We hope that this Q&A article has addressed some of the most frequently asked questions about solving the equation.

Tips and Tricks

• When working with fractions, it's essential to simplify the equation by eliminating the denominator.
• Multiplying both sides of the equation by a variable can help eliminate the fraction.
• Dividing both sides of the equation by a constant can help isolate the variable.

Real-World Applications

Solving equations is a fundamental concept in mathematics, and it has numerous real-world applications. In physics, equations are used to describe the motion of objects, while in engineering, equations are used to design and optimize systems. In finance, equations are used to model and analyze financial data.

Common Mistakes

• Failing to simplify the equation by eliminating the denominator.
• Multiplying both sides of the equation by a variable without considering the implications.
• Dividing both sides of the equation by a constant without considering the implications.

Conclusion

Solving the equation $\frac{3}{-y} - 9 = 7$ requires a deep understanding of algebraic operations and techniques. By following the step-by-step approach outlined in this article, readers can simplify the equation and solve for $y$. We hope that this Q&A article has addressed some of the most frequently asked questions about solving the equation.