Consider The Equation 3 P − 7 + P = 13 3p - 7 + P = 13 3 P − 7 + P = 13 . What Is The Resulting Equation After The First Step In The Solution?A. P − 7 = 13 − 3 P P - 7 = 13 - 3p P − 7 = 13 − 3 P B. 2 P − 7 = 13 2p - 7 = 13 2 P − 7 = 13 C. 3 P − 7 = 13 − P 3p - 7 = 13 - P 3 P − 7 = 13 − P D. 4 P − 7 = 13 4p - 7 = 13 4 P − 7 = 13

Introduction

Linear equations are a fundamental concept in mathematics, and solving them is a crucial skill for students to master. In this article, we will focus on solving a specific linear equation, step by step, to understand the process and arrive at the correct solution.

The Given Equation

The given equation is $3p - 7 + p = 13$. Our goal is to simplify this equation and find the value of $p$.

Step 1: Combine Like Terms

The first step in solving this equation is to combine like terms. In this case, we have two terms with the variable $p$, which are $3p$ and $p$. We can combine these terms by adding their coefficients.

3p + p = 4p

So, the equation becomes:

$$4p - 7 = 13$$

The Resulting Equation

After combining like terms, the resulting equation is:

$$4p - 7 = 13$$

This is the equation we get after the first step in the solution.

Comparing with the Options

Now, let's compare the resulting equation with the options provided:

A. $p - 7 = 13 - 3p$ B. $2p - 7 = 13$ C. $3p - 7 = 13 - p$ D. $4p - 7 = 13$

The correct option is:

D. $4p - 7 = 13$

Conclusion

In this article, we solved a linear equation step by step, starting with combining like terms. We arrived at the resulting equation after the first step in the solution, which is $4p - 7 = 13$. This equation is a crucial step in solving the original equation and finding the value of $p$.

Tips and Tricks

• When solving linear equations, always start by combining like terms.
• Use the distributive property to simplify expressions.
• Check your work by plugging the solution back into the original equation.

Common Mistakes

• Failing to combine like terms.
• Not using the distributive property to simplify expressions.
• Not checking the solution by plugging it back into the original equation.

Real-World Applications

Linear equations have numerous real-world applications, including:

• Physics: Solving linear equations is essential in physics to describe the motion of objects.
• Engineering: Linear equations are used to design and optimize systems.
• Economics: Linear equations are used to model economic systems and make predictions.

Practice Problems

Try solving the following linear equations:

1. $2x + 5 = 11$
2. $x - 3 = 7$
3. $3x + 2 = 14$

References

• [1] "Linear Equations" by Khan Academy
• [2] "Solving Linear Equations" by Math Open Reference
• [3] "Linear Equations in One Variable" by Purplemath
  Solving Linear Equations: A Q&A Guide =====================================

Introduction

Linear equations are a fundamental concept in mathematics, and solving them is a crucial skill for students to master. In this article, we will provide a Q&A guide to help students understand the process of solving linear equations.

Q: What is a linear equation?

A: A linear equation is an equation in which the highest power of the variable (usually x) is 1. It can be written in the form ax + b = c, where a, b, and c are constants.

Q: What are the steps to solve a linear equation?

A: The steps to solve a linear equation are:

1. Combine like terms.
2. Isolate the variable (usually x) on one side of the equation.
3. Check the solution by plugging it back into the original equation.

Q: What is the distributive property?

A: The distributive property is a rule that allows us to multiply a single term to multiple terms inside parentheses. It can be written as:

a(b + c) = ab + ac

Q: How do I use the distributive property to simplify expressions?

A: To use the distributive property to simplify expressions, follow these steps:

1. Identify the terms inside the parentheses.
2. Multiply the single term outside the parentheses to each term inside the parentheses.
3. Combine like terms.

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 (usually x) is 1. A quadratic equation is an equation in which the highest power of the variable (usually x) is 2.

Q: How do I solve a linear equation with fractions?

A: To solve a linear equation with fractions, follow these steps:

1. Multiply both sides of the equation by the least common multiple (LCM) of the denominators.
2. Combine like terms.
3. Isolate the variable (usually x) on one side of the equation.

Q: What is the order of operations?

A: The order of operations is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. The order of operations is:

1. Parentheses
2. Exponents
3. Multiplication and Division (from left to right)
4. Addition and Subtraction (from left to right)

Q: How do I check my solution to a linear equation?

A: To check your solution to a linear equation, follow these steps:

1. Plug the solution back into the original equation.
2. Simplify the expression.
3. Check if the equation is true.

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

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

• Failing to combine like terms.
• Not using the distributive property to simplify expressions.
• Not checking the solution by plugging it back into the original equation.

Q: How do I apply linear equations to real-world problems?

A: Linear equations can be applied to real-world problems in a variety of ways, including:

• Physics: Solving linear equations is essential in physics to describe the motion of objects.
• Engineering: Linear equations are used to design and optimize systems.
• Economics: Linear equations are used to model economic systems and make predictions.

Conclusion

In this article, we provided a Q&A guide to help students understand the process of solving linear equations. We covered topics such as the distributive property, linear equations with fractions, and the order of operations. We also discussed common mistakes to avoid and how to apply linear equations to real-world problems.