Solve For $p$. P 2 − 2 = 8 \frac{p}{2} - 2 = 8 2 P − 2 = 8

Mar 10, 2025 by ADMIN 63 views

$Solve for $p$: $\frac{p}{2} - 2 = 8$$

Introduction

Solving for a variable in an equation is a fundamental concept in mathematics, and it's essential to understand how to isolate the variable to find its value. In this article, we will focus on solving for the variable $p$ in the given equation $\frac{p}{2} - 2 = 8$ . We will break down the steps involved in solving this equation and provide a clear explanation of each step.

Understanding the Equation

The given equation is $\frac{p}{2} - 2 = 8$ . To solve for $p$ , we need to isolate the variable $p$ on one side of the equation. The equation involves a fraction, so we will need to use algebraic techniques to simplify and solve it.

Step 1: Add 2 to Both Sides of the Equation

The first step in solving the equation is to add 2 to both sides of the equation to get rid of the negative term. This will help us simplify the equation and make it easier to solve.

$\frac{p}{2} - 2 + 2 = 8 + 2$

Simplifying the equation, we get:

$\frac{p}{2} = 10$

Step 2: Multiply Both Sides of the Equation by 2

To isolate the variable $p$ , we need to get rid of the fraction. We can do this by multiplying both sides of the equation by 2.

$\frac{p}{2} \times 2 = 10 \times 2$

Simplifying the equation, we get:

$p = 20$

Conclusion

In this article, we solved for the variable $p$ in the given equation $\frac{p}{2} - 2 = 8$ . We broke down the steps involved in solving the equation and provided a clear explanation of each step. By following these steps, we were able to isolate the variable $p$ and find its value.

Tips and Tricks

When solving an equation with a fraction, it's essential to get rid of the fraction by multiplying both sides of the equation by the denominator.
Adding or subtracting the same value to both sides of the equation is a common technique used to simplify the equation and isolate the variable.
When multiplying both sides of the equation by a value, make sure to multiply both sides by the same value to maintain the equality of the equation.

Real-World Applications

Solving for a variable in an equation is a fundamental concept in mathematics, and it has numerous real-world applications. Here are a few examples:

In physics, solving for a variable in an equation can help us understand the motion of objects and predict their behavior.
In engineering, solving for a variable in an equation can help us design and optimize systems and structures.
In finance, solving for a variable in an equation can help us understand the behavior of financial markets and make informed investment decisions.

Common Mistakes to Avoid

When solving for a variable in an equation, there are several common mistakes to avoid. Here are a few examples:

Not getting rid of the fraction by multiplying both sides of the equation by the denominator.
Not adding or subtracting the same value to both sides of the equation.
Not multiplying both sides of the equation by the same value.

Final Thoughts

Solving for a variable in an equation is a fundamental concept in mathematics, and it's essential to understand how to isolate the variable to find its value. By following the steps outlined in this article, you can solve for a variable in an equation and apply the concepts to real-world problems. Remember to get rid of the fraction, add or subtract the same value to both sides of the equation, and multiply both sides of the equation by the same value to maintain the equality of the equation.

Introduction

In our previous article, we solved for the variable $p$ in the given equation $\frac{p}{2} - 2 = 8$ . We broke down the steps involved in solving the equation and provided a clear explanation of each step. In this article, we will answer some of the most frequently asked questions related to solving for a variable in an equation.

Q&A

Q: What is the first step in solving an equation with a fraction?

A: The first step in solving an equation with a fraction is to get rid of the fraction by multiplying both sides of the equation by the denominator.

Q: How do I get rid of a negative term in an equation?

A: To get rid of a negative term in an equation, you can add the same value to both sides of the equation. For example, if you have the equation $x - 3 = 5$ , you can add 3 to both sides to get $x = 8$ .

Q: What is the difference between adding and subtracting the same value to both sides of an equation?

A: Adding and subtracting the same value to both sides of an equation are two different operations. Adding the same value to both sides of an equation is used to get rid of a negative term, while subtracting the same value from both sides of an equation is used to get rid of a positive term.

Q: How do I multiply both sides of an equation by a value?

A: To multiply both sides of an equation by a value, you can simply multiply both sides by that value. For example, if you have the equation $x = 5$ and you want to multiply both sides by 2, you can multiply both sides by 2 to get $2x = 10$ .

Q: What is the importance of maintaining the equality of an equation?

A: Maintaining the equality of an equation is crucial when solving for a variable. If you multiply both sides of an equation by a value, you must multiply both sides by the same value to maintain the equality of the equation.

Q: Can I use a calculator to solve for a variable in an equation?

A: Yes, you can use a calculator to solve for a variable in an equation. However, it's essential to understand the steps involved in solving the equation and to verify the solution using a calculator.

Q: How do I check if my solution is correct?

A: To check if your solution is correct, you can plug the solution back into the original equation and verify that it's true. For example, if you have the equation $x = 5$ and you plug $x = 5$ back into the equation, you should get a true statement.