Solve For $v$.$\[ \begin{align*} 2v - V &= 11 \\ v &= \square \end{align*} \\]

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 simple linear equation to find the value of the variable $v$. We will break down the solution step by step, making it easy to understand and follow.

The Equation

The given equation is:

$$2v - v = 11$$

Our goal is to solve for $v$, which means we need to isolate the variable $v$ on one side of the equation.

Step 1: Combine Like Terms

The first step in solving the equation is to combine like terms. In this case, we have two terms with the variable $v$: $2v$ and $-v$. We can combine these terms by adding their coefficients:

$$2v - v = (2 - 1)v = 1v = v$$

So, the equation becomes:

$$v = 11$$

Step 2: Solve for $v$

Now that we have simplified the equation, we can solve for $v$ by dividing both sides of the equation by 1:

$$\frac{v}{1} = \frac{11}{1}$$

This simplifies to:

$$v = 11$$

Conclusion

In this article, we solved a simple linear equation to find the value of the variable $v$. We broke down the solution into two steps: combining like terms and solving for $v$. By following these steps, we were able to isolate the variable $v$ and find its value.

Tips and Tricks

• When solving linear equations, always start by combining like terms.
• Use the order of operations (PEMDAS) to simplify the equation.
• Make sure to isolate the variable on one side of the equation.
• Check your solution by plugging it back into the original equation.

Real-World Applications

Linear equations have many real-world applications, such as:

• Modeling population growth
• Calculating interest rates
• Determining the cost of goods
• Solving problems in physics and engineering

Practice Problems

Try solving the following linear equations:

1. $2x + 3 = 7$
2. $x - 2 = 5$
3. $3x = 12$

Answer Key

1. $x = 2$
2. $x = 7$
3. $x = 4$

Conclusion

Introduction

In our previous article, we solved a simple linear equation to find the value of the variable $v$. In this article, we will provide a Q&A guide to help you understand and apply the concepts 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(s) is 1. It can be written in the form $ax + b = c$, where $a$, $b$, and $c$ are constants, and $x$ is the variable.

Q: How do I solve a linear equation?

A: To solve a linear equation, you need to isolate the variable on one side of the equation. You can do this by using the following steps:

1. Combine like terms.
2. Use the order of operations (PEMDAS) to simplify the equation.
3. Add or subtract the same value to both sides of the equation to isolate the variable.
4. Divide both sides of the equation by the coefficient of the variable to solve for it.

Q: What is the order of operations (PEMDAS)?

A: The order of operations (PEMDAS) is a set of rules that tells you which operations to perform first when you have multiple operations in an expression. The acronym PEMDAS stands for:

1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next.
3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: How do I combine like terms?

A: To combine like terms, you need to add or subtract the coefficients of the terms with the same variable. For example, if you have the expression $2x + 3x$, you can combine the like terms by adding the coefficients:

$$2x + 3x = (2 + 3)x = 5x$$

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(s) is 1. A quadratic equation, on the other hand, is an equation in which the highest power of the variable(s) is 2. For example:

Linear equation: $2x + 3 = 5$ Quadratic equation: $x^2 + 4x + 4 = 0$

Q: Can I use a calculator to solve linear equations?

A: Yes, you can use a calculator to solve linear equations. However, it's always a good idea to check your solution by plugging it back into the original equation to make sure it's correct.

Q: How do I check my solution?

A: To check your solution, you need to plug it back into the original equation and make sure it's true. For example, if you solved the equation $2x + 3 = 5$ and got $x = 1$, you would plug $x = 1$ back into the original equation to check:

$$2(1) + 3 = 5$$

$$2 + 3 = 5$$

$$5 = 5$$

Since the equation is true, your solution is correct.

Conclusion

Solving linear equations is an essential skill for students to master. By following the steps outlined in this article and practicing with different types of equations, you can become proficient in solving linear equations and apply them to a wide range of problems. Remember to always combine like terms, use the order of operations, and isolate the variable on one side of the equation. With practice, you will become proficient in solving linear equations and be able to apply them to real-world problems.