Solve For X X X . Show Each Step Of The Solution. 4.5 ( 8 − X ) + 36 = 102 − 2.5 ( 3 X + 24 4.5(8-x) + 36 = 102 - 2.5(3x + 24 4.5 ( 8 − X ) + 36 = 102 − 2.5 ( 3 X + 24 ]

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Introduction

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Solving for $x$ in a linear equation can be a daunting task, especially when the equation is complex and involves multiple operations. However, with a clear understanding of the steps involved and a systematic approach, solving for $x$ can be a straightforward process. In this article, we will guide you through the step-by-step solution of the equation $4.5(8-x) + 36 = 102 - 2.5(3x + 24)$.

Understanding the Equation

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The given equation is $4.5(8-x) + 36 = 102 - 2.5(3x + 24)$. To solve for $x$, we need to simplify the equation by applying the distributive property, combining like terms, and isolating the variable $x$.

Step 1: Apply the Distributive Property

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The first step in solving the equation is to apply the distributive property to expand the terms inside the parentheses.

4.5(8-x) = 4.5(8) - 4.5x
= 36 - 4.5x

Similarly, we apply the distributive property to the second term on the right-hand side of the equation.

-2.5(3x + 24) = -2.5(3x) - 2.5(24)
= -7.5x - 60

Step 2: Combine Like Terms

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Now that we have expanded the terms inside the parentheses, we can combine like terms to simplify the equation.

36 - 4.5x + 36 = 102 - 7.5x - 60
72 - 4.5x = 42 - 7.5x

Step 3: Isolate the Variable $x$

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To isolate the variable $x$, we need to get all the terms involving $x$ on one side of the equation and the constant terms on the other side.

72 - 4.5x = 42 - 7.5x
72 - 42 = -7.5x + 4.5x
30 = -3x

Step 4: Solve for $x$

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Finally, we can solve for $x$ by dividing both sides of the equation by the coefficient of $x$.

30 = -3x
x = -30/3
x = -10

Conclusion

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In this article, we have walked you through the step-by-step solution of the equation $4.5(8-x) + 36 = 102 - 2.5(3x + 24)$. By applying the distributive property, combining like terms, and isolating the variable $x$, we have arrived at the solution $x = -10$. We hope this guide has been helpful in understanding the process of solving for $x$ in a linear equation.

Frequently Asked Questions

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Q: What is the distributive property?

A: The distributive property is a mathematical property that allows us to expand the terms inside the parentheses by multiplying each term inside the parentheses by the coefficient outside the parentheses.

Q: How do I combine like terms?

A: To combine like terms, we need to add or subtract the coefficients of the terms with the same variable.

Q: How do I isolate the variable $x$?

A: To isolate the variable $x$, we need to get all the terms involving $x$ on one side of the equation and the constant terms on the other side.

Additional Resources

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If you are struggling to solve for $x$ in a linear equation, we recommend checking out the following resources:

• Khan Academy: Linear Equations
• Mathway: Solve for $x$
• Wolfram Alpha: Solve for $x$

We hope this article has been helpful in understanding the process of solving for $x$ in a linear equation. If you have any further questions or need additional assistance, please don't hesitate to ask.

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===========================================================

Introduction

---

Solving for $x$ in a linear equation can be a daunting task, especially when the equation is complex and involves multiple operations. However, with a clear understanding of the steps involved and a systematic approach, solving for $x$ can be a straightforward process. In this article, we will guide you through the step-by-step solution of the equation $4.5(8-x) + 36 = 102 - 2.5(3x + 24)$ and provide answers to frequently asked questions.

Q&A: Solving for $x$

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Q: What is the distributive property?

A: The distributive property is a mathematical property that allows us to expand the terms inside the parentheses by multiplying each term inside the parentheses by the coefficient outside the parentheses.

Q: How do I apply the distributive property to the equation?

A: To apply the distributive property, we need to multiply each term inside the parentheses by the coefficient outside the parentheses. For example, in the equation $4.5(8-x) + 36 = 102 - 2.5(3x + 24)$, we would multiply $4.5$ by $8$ and $-x$ to get $36 - 4.5x$.

Q: How do I combine like terms?

A: To combine like terms, we need to add or subtract the coefficients of the terms with the same variable. For example, in the equation $72 - 4.5x = 42 - 7.5x$, we can combine the constant terms $72$ and $42$ to get $114$, and combine the terms involving $x$ to get $-12x$.

Q: How do I isolate the variable $x$?

A: To isolate the variable $x$, we need to get all the terms involving $x$ on one side of the equation and the constant terms on the other side. For example, in the equation $72 - 4.5x = 42 - 7.5x$, we can add $7.5x$ to both sides of the equation to get $72 - 4.5x + 7.5x = 42$, and then combine like terms to get $72 + 2.5x = 42$.

Q: How do I solve for $x$?

A: To solve for $x$, we need to isolate the variable $x$ by getting all the terms involving $x$ on one side of the equation and the constant terms on the other side. For example, in the equation $72 + 2.5x = 42$, we can subtract $72$ from both sides of the equation to get $2.5x = -30$, and then divide both sides of the equation by $2.5$ to get $x = -12$.

Q&A: Common Mistakes

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Q: What are some common mistakes to avoid when solving for $x$?

A: Some common mistakes to avoid when solving for $x$ include:

• Not applying the distributive property correctly
• Not combining like terms correctly
• Not isolating the variable $x$ correctly
• Not solving for $x$ correctly

Q: How can I avoid these mistakes?

A: To avoid these mistakes, make sure to:

• Apply the distributive property correctly by multiplying each term inside the parentheses by the coefficient outside the parentheses
• Combine like terms correctly by adding or subtracting the coefficients of the terms with the same variable
• Isolate the variable $x$ correctly by getting all the terms involving $x$ on one side of the equation and the constant terms on the other side
• Solve for $x$ correctly by dividing both sides of the equation by the coefficient of $x$

Q&A: Additional Resources

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Q: Where can I find additional resources to help me solve for $x$?

A: There are many resources available to help you solve for $x$, including:

• Khan Academy: Linear Equations
• Mathway: Solve for $x$
• Wolfram Alpha: Solve for $x$

Q: What are some tips for using these resources?

A: Some tips for using these resources include:

• Make sure to read the instructions carefully before using the resource
• Practice solving for $x$ using the resource to build your skills and confidence
• Don't be afraid to ask for help if you get stuck or have questions

Conclusion

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Solving for $x$ in a linear equation can be a daunting task, but with a clear understanding of the steps involved and a systematic approach, it can be a straightforward process. By applying the distributive property, combining like terms, and isolating the variable $x$, we can solve for $x$ and arrive at the solution. We hope this article has been helpful in understanding the process of solving for $x$ and providing answers to frequently asked questions. If you have any further questions or need additional assistance, please don't hesitate to ask.