Solve For P P P .${ 0.81(p - 3) = 7.29 }$p = \square$

Solving for $p$: A Step-by-Step Guide to Isolating the Variable

Introduction

In algebra, solving for a variable is a crucial skill that helps us find the value of a unknown quantity. In this article, we will focus on solving for $p$ in the given equation $0.81(p - 3) = 7.29$. We will break down the solution into manageable steps, making it easy to understand and follow along.

Understanding the Equation

The given equation is $0.81(p - 3) = 7.29$. To solve for $p$, we need to isolate the variable $p$ on one side of the equation. The equation involves a decimal coefficient, which can be challenging to work with. However, with the right approach, we can simplify the equation and find the value of $p$.

Step 1: Distribute the Decimal Coefficient

To start solving the equation, we need to distribute the decimal coefficient $0.81$ to the terms inside the parentheses. This will help us simplify the equation and make it easier to work with.

0.81(p - 3) = 7.29
0.81p - 2.43 = 7.29

Step 2: Add 2.43 to Both Sides

Now that we have distributed the decimal coefficient, we need to add $2.43$ to both sides of the equation. This will help us eliminate the negative term and isolate the variable $p$.

0.81p - 2.43 + 2.43 = 7.29 + 2.43
0.81p = 9.72

Step 3: Divide Both Sides by 0.81

To find the value of $p$, we need to divide both sides of the equation by $0.81$. This will help us isolate the variable $p$ and find its value.

\frac{0.81p}{0.81} = \frac{9.72}{0.81}
p = 12

Conclusion

In this article, we solved for $p$ in the given equation $0.81(p - 3) = 7.29$. We broke down the solution into manageable steps, making it easy to understand and follow along. By distributing the decimal coefficient, adding $2.43$ to both sides, and dividing both sides by $0.81$, we were able to isolate the variable $p$ and find its value.

Final Answer

The final answer is $p = 12$.

Related Topics

• Solving linear equations
• Distributing decimal coefficients
• Isolating variables
• Algebraic manipulations

Resources

• Khan Academy: Solving Linear Equations
• Mathway: Solving Linear Equations
• Algebra.com: Solving Linear Equations

FAQs

• Q: What is the value of $p$ in the equation $0.81(p - 3) = 7.29$? A: The value of $p$ is $12$.
• Q: How do I solve for $p$ in a linear equation? A: To solve for $p$, you need to isolate the variable $p$ on one side of the equation. You can do this by distributing decimal coefficients, adding or subtracting terms, and dividing both sides by the coefficient of $p$.
• Q: What are some common mistakes to avoid when solving for $p$? A: Some common mistakes to avoid when solving for $p$ include forgetting to distribute decimal coefficients, adding or subtracting terms incorrectly, and dividing both sides by the wrong coefficient.
  Solving for $p$: A Q&A Guide to Isolating the Variable

Introduction

In our previous article, we solved for $p$ in the equation $0.81(p - 3) = 7.29$. We broke down the solution into manageable steps, making it easy to understand and follow along. In this article, we will provide a Q&A guide to help you better understand the concept of solving for $p$ and how to apply it to different types of equations.

Q&A: Solving for $p$

Q: What is the first step in solving for $p$ in a linear equation?

A: The first step in solving for $p$ is to distribute the decimal coefficient to the terms inside the parentheses. This will help you simplify the equation and make it easier to work with.

Q: How do I distribute a decimal coefficient to the terms inside the parentheses?

A: To distribute a decimal coefficient, you need to multiply the coefficient by each term inside the parentheses. For example, if you have the equation $0.81(p - 3) = 7.29$, you would multiply $0.81$ by $p$ and $-3$ to get $0.81p - 2.43$.

Q: What is the next step in solving for $p$ after distributing the decimal coefficient?

A: After distributing the decimal coefficient, you need to add or subtract terms to isolate the variable $p$. This may involve adding or subtracting a constant term to both sides of the equation.

Q: How do I add or subtract terms to isolate the variable $p$?

A: To add or subtract terms, you need to follow the order of operations (PEMDAS). This means that you need to perform any calculations inside parentheses first, followed by any exponents, then multiplication and division, and finally addition and subtraction.

Q: What is the final step in solving for $p$?

A: The final step in solving for $p$ is to divide both sides of the equation by the coefficient of $p$. This will help you isolate the variable $p$ and find its value.

Q: How do I divide both sides of the equation by the coefficient of $p$?

A: To divide both sides of the equation by the coefficient of $p$, you need to follow the rules of division. This means that you need to divide each term on both sides of the equation by the coefficient of $p$.

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

A: Some common mistakes to avoid when solving for $p$ include forgetting to distribute decimal coefficients, adding or subtracting terms incorrectly, and dividing both sides by the wrong coefficient.

Q&A: Algebraic Manipulations

Q: What is the difference between a linear equation and a quadratic equation?

A: A linear equation is an equation in which the highest power of the variable is 1. A quadratic equation is an equation in which the highest power of the variable is 2.

Q: How do I solve a quadratic equation?

A: To solve a quadratic equation, you need to use the quadratic formula. The quadratic formula is given by $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$, where $a$, $b$, and $c$ are the coefficients of the quadratic equation.

Q: What is the quadratic formula?

A: The quadratic formula is a mathematical formula that is used to solve quadratic equations. It is given by $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$, where $a$, $b$, and $c$ are the coefficients of the quadratic equation.

Q&A: Real-World Applications

Q: How do I apply the concept of solving for $p$ to real-world problems?

A: To apply the concept of solving for $p$ to real-world problems, you need to identify the variable $p$ and the equation that it is part of. You can then use the steps outlined above to solve for $p$ and find its value.

Q: What are some examples of real-world problems that involve solving for $p$?

A: Some examples of real-world problems that involve solving for $p$ include calculating the cost of a product, determining the amount of time it takes to complete a task, and finding the value of a variable in a scientific equation.

Conclusion

In this article, we provided a Q&A guide to help you better understand the concept of solving for $p$ and how to apply it to different types of equations. We covered topics such as algebraic manipulations, quadratic equations, and real-world applications. By following the steps outlined above, you can solve for $p$ and find its value in a variety of situations.

Final Answer

The final answer is $p = 12$.

Related Topics

• Solving linear equations
• Distributing decimal coefficients
• Isolating variables
• Algebraic manipulations
• Quadratic equations
• Real-world applications

Resources

• Khan Academy: Solving Linear Equations
• Mathway: Solving Linear Equations
• Algebra.com: Solving Linear Equations
• Wolfram Alpha: Quadratic Formula
• Khan Academy: Quadratic Equations

FAQs

• Q: What is the value of $p$ in the equation $0.81(p - 3) = 7.29$? A: The value of $p$ is $12$.
• Q: How do I solve for $p$ in a linear equation? A: To solve for $p$, you need to isolate the variable $p$ on one side of the equation. You can do this by distributing decimal coefficients, adding or subtracting terms, and dividing both sides by the coefficient of $p$.
• Q: What are some common mistakes to avoid when solving for $p$? A: Some common mistakes to avoid when solving for $p$ include forgetting to distribute decimal coefficients, adding or subtracting terms incorrectly, and dividing both sides by the wrong coefficient.