Solve The Equation: { (2y - 3 \times 3) = -(8 + 9y - 8) + 68$}$

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Introduction

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In this article, we will delve into the world of algebra and solve a complex equation step by step. The equation we will be solving is: $(2y - 3 \times 3) = -(8 + 9y - 8) + 68$. This equation involves various mathematical operations, including multiplication, addition, and subtraction. Our goal is to isolate the variable $y$ and find its value.

Understanding the Equation

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Before we begin solving the equation, let's break it down and understand its components. The equation is: $(2y - 3 \times 3) = -(8 + 9y - 8) + 68$. We can see that it involves the following operations:

• Multiplication: $3 \times 3$
• Addition: $8 + 9y - 8$
• Subtraction: $-(8 + 9y - 8)$
• Isolation of the variable $y$

Step 1: Simplify the Left Side of the Equation

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The first step in solving the equation is to simplify the left side. We can start by evaluating the expression $3 \times 3$, which equals $9$. So, the left side of the equation becomes: $2y - 9$.

Step 2: Simplify the Right Side of the Equation

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Next, we need to simplify the right side of the equation. We can start by evaluating the expression $-(8 + 9y - 8)$. This expression can be simplified as follows:

• First, we can combine the constants $8$ and $-8$, which cancel each other out.
• Next, we can distribute the negative sign to the terms inside the parentheses, which gives us: $-9y - 8$.
• Finally, we can add $68$ to the expression, which gives us: $-9y + 60$.

Step 3: Set Up the Equation with the Simplified Sides

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Now that we have simplified both sides of the equation, we can set up the equation as follows:

$2y - 9 = -9y + 60$

Step 4: Add $9y$ to Both Sides of the Equation

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To isolate the variable $y$, we need to get all the terms involving $y$ on one side of the equation. We can do this by adding $9y$ to both sides of the equation. This gives us:

$2y + 9y - 9 = -9y + 9y + 60$

Step 5: Combine Like Terms

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Next, we can combine like terms on both sides of the equation. On the left side, we have $2y + 9y$, which equals $11y$. On the right side, we have $-9y + 9y$, which equals $0$. So, the equation becomes:

$11y - 9 = 60$

Step 6: Add $9$ to Both Sides of the Equation

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To isolate the variable $y$, we need to get rid of the constant term on the left side of the equation. We can do this by adding $9$ to both sides of the equation. This gives us:

$11y - 9 + 9 = 60 + 9$

Step 7: Simplify the Equation

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Now that we have added $9$ to both sides of the equation, we can simplify the equation. On the left side, we have $-9 + 9$, which equals $0$. On the right side, we have $60 + 9$, which equals $69$. So, the equation becomes:

$11y = 69$

Step 8: Divide Both Sides of the Equation by $11$

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Finally, we can solve for the variable $y$ by dividing both sides of the equation by $11$. This gives us:

$y = \frac{69}{11}$

Conclusion

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In this article, we solved the equation $(2y - 3 \times 3) = -(8 + 9y - 8) + 68$ step by step. We simplified both sides of the equation, isolated the variable $y$, and found its value. The final answer is $y = \frac{69}{11}$.

Frequently Asked Questions

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Q: What is the value of $y$ in the equation $(2y - 3 \times 3) = -(8 + 9y - 8) + 68$?

A: The value of $y$ is $\frac{69}{11}$.

Q: How do I simplify the left side of the equation $(2y - 3 \times 3) = -(8 + 9y - 8) + 68$?

A: To simplify the left side of the equation, you can evaluate the expression $3 \times 3$, which equals $9$. So, the left side of the equation becomes: $2y - 9$.

Q: How do I simplify the right side of the equation $(2y - 3 \times 3) = -(8 + 9y - 8) + 68$?

A: To simplify the right side of the equation, you can evaluate the expression $-(8 + 9y - 8)$, which equals $-9y - 8$. Then, you can add $68$ to the expression, which gives you: $-9y + 60$.

Q: How do I isolate the variable $y$ in the equation $(2y - 3 \times 3) = -(8 + 9y - 8) + 68$?

A: To isolate the variable $y$, you can add $9y$ to both sides of the equation, which gives you: $11y - 9 = 60$. Then, you can add $9$ to both sides of the equation, which gives you: $11y = 69$. Finally, you can divide both sides of the equation by $11$, which gives you: $y = \frac{69}{11}$.

References

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• Algebra
• Equations
• Variables
  

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Introduction

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In our previous article, we solved the equation $(2y - 3 \times 3) = -(8 + 9y - 8) + 68$ step by step. We simplified both sides of the equation, isolated the variable $y$, and found its value. In this article, we will provide a Q&A guide to help you understand the solution and answer any questions you may have.

Q&A Guide

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Q: What is the value of $y$ in the equation $(2y - 3 \times 3) = -(8 + 9y - 8) + 68$?

A: The value of $y$ is $\frac{69}{11}$.

Q: How do I simplify the left side of the equation $(2y - 3 \times 3) = -(8 + 9y - 8) + 68$?

A: To simplify the left side of the equation, you can evaluate the expression $3 \times 3$, which equals $9$. So, the left side of the equation becomes: $2y - 9$.

Q: How do I simplify the right side of the equation $(2y - 3 \times 3) = -(8 + 9y - 8) + 68$?

A: To simplify the right side of the equation, you can evaluate the expression $-(8 + 9y - 8)$, which equals $-9y - 8$. Then, you can add $68$ to the expression, which gives you: $-9y + 60$.

Q: How do I isolate the variable $y$ in the equation $(2y - 3 \times 3) = -(8 + 9y - 8) + 68$?

A: To isolate the variable $y$, you can add $9y$ to both sides of the equation, which gives you: $11y - 9 = 60$. Then, you can add $9$ to both sides of the equation, which gives you: $11y = 69$. Finally, you can divide both sides of the equation by $11$, which gives you: $y = \frac{69}{11}$.

Q: What is the process of solving an equation?

A: The process of solving an equation involves simplifying both sides of the equation, isolating the variable, and finding its value. This can involve various mathematical operations, including addition, subtraction, multiplication, and division.

Q: How do I know if I have solved the equation correctly?

A: To ensure that you have solved the equation correctly, you can check your work by plugging the value of the variable back into the original equation. If the equation holds true, then you have solved it correctly.

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

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

• Not simplifying both sides of the equation
• Not isolating the variable
• Not checking your work
• Not using the correct mathematical operations

Tips and Tricks

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• Always simplify both sides of the equation before isolating the variable.
• Use the correct mathematical operations to isolate the variable.
• Check your work by plugging the value of the variable back into the original equation.
• Avoid common mistakes, such as not simplifying both sides of the equation or not isolating the variable.

Conclusion

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Solving equations can be a challenging task, but with practice and patience, you can become proficient in solving even the most complex equations. Remember to simplify both sides of the equation, isolate the variable, and check your work to ensure that you have solved the equation correctly. If you have any questions or need further assistance, don't hesitate to ask.

Frequently Asked Questions

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Q: What is the value of $y$ in the equation $(2y - 3 \times 3) = -(8 + 9y - 8) + 68$?

A: The value of $y$ is $\frac{69}{11}$.

Q: How do I simplify the left side of the equation $(2y - 3 \times 3) = -(8 + 9y - 8) + 68$?

A: To simplify the left side of the equation, you can evaluate the expression $3 \times 3$, which equals $9$. So, the left side of the equation becomes: $2y - 9$.

Q: How do I simplify the right side of the equation $(2y - 3 \times 3) = -(8 + 9y - 8) + 68$?

A: To simplify the right side of the equation, you can evaluate the expression $-(8 + 9y - 8)$, which equals $-9y - 8$. Then, you can add $68$ to the expression, which gives you: $-9y + 60$.

Q: How do I isolate the variable $y$ in the equation $(2y - 3 \times 3) = -(8 + 9y - 8) + 68$?

A: To isolate the variable $y$, you can add $9y$ to both sides of the equation, which gives you: $11y - 9 = 60$. Then, you can add $9$ to both sides of the equation, which gives you: $11y = 69$. Finally, you can divide both sides of the equation by $11$, which gives you: $y = \frac{69}{11}$.

References

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• Algebra
• Equations
• Variables