Solve For V V V . ${ -5 = V - \frac{3}{4} }$ Simplify Your Answer As Much As Possible. ${ V = }$

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Introduction

In mathematics, solving for a variable is a fundamental concept that involves isolating the variable on one side of the equation. In this article, we will focus on solving for $v$ in the given equation: $-5 = v - \frac{3}{4}$. We will break down the solution into manageable steps and provide a clear explanation of each step.

Step 1: Add $\frac{3}{4}$ to Both Sides

To solve for $v$, we need to isolate the variable on one side of the equation. The first step is to add $\frac{3}{4}$ to both sides of the equation. This will help us get rid of the fraction on the right-hand side.

{ -5 = v - \frac{3}{4} \}

{ -5 + \frac{3}{4} = v - \frac{3}{4} + \frac{3}{4} \}

{ -5 + \frac{3}{4} = v \}

Step 2: Simplify the Left-Hand Side

Now that we have added $\frac{3}{4}$ to both sides, we can simplify the left-hand side of the equation. To do this, we need to find a common denominator for $-5$ and $\frac{3}{4}$. The common denominator is $4$, so we can rewrite $-5$ as $-\frac{20}{4}$.

{ -\frac{20}{4} + \frac{3}{4} = v \}

{ -\frac{17}{4} = v \}

Conclusion

In this article, we have solved for $v$ in the given equation: $-5 = v - \frac{3}{4}$. We broke down the solution into manageable steps and provided a clear explanation of each step. By following these steps, we were able to isolate the variable $v$ on one side of the equation and simplify the left-hand side.

Final Answer

The final answer is: $\boxed{-\frac{17}{4}}$

Why is Solving for $v$ Important?

Solving for $v$ is an important concept in mathematics because it helps us understand how to isolate variables on one side of an equation. This skill is essential in solving a wide range of mathematical problems, from simple algebraic equations to complex calculus problems.

Real-World Applications

Solving for $v$ has many real-world applications. For example, in physics, solving for velocity is crucial in understanding the motion of objects. In economics, solving for variables is essential in understanding the behavior of markets and making informed decisions.

Tips and Tricks

Here are some tips and tricks to help you solve for $v$:

• Always start by isolating the variable on one side of the equation.
• Use inverse operations to get rid of fractions and decimals.
• Simplify the left-hand side of the equation by finding a common denominator.
• Check your work by plugging the solution back into the original equation.

Common Mistakes to Avoid

Here are some common mistakes to avoid when solving for $v$:

• Not isolating the variable on one side of the equation.
• Not using inverse operations to get rid of fractions and decimals.
• Not simplifying the left-hand side of the equation.
• Not checking your work by plugging the solution back into the original equation.

Conclusion

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Introduction

In our previous article, we discussed how to solve for $v$ in the equation $-5 = v - \frac{3}{4}$. In this article, we will provide a Q&A guide to help you better understand the concept of solving for $v$.

Q: What is solving for $v$?

A: Solving for $v$ is a mathematical concept that involves isolating the variable $v$ on one side of an equation. This means that we need to get rid of any constants or other variables that are attached to $v$.

Q: Why is solving for $v$ important?

A: Solving for $v$ is important because it helps us understand how to isolate variables on one side of an equation. This skill is essential in solving a wide range of mathematical problems, from simple algebraic equations to complex calculus problems.

Q: How do I solve for $v$?

A: To solve for $v$, you need to follow these steps:

1. Isolate the variable $v$ on one side of the equation.
2. Use inverse operations to get rid of fractions and decimals.
3. Simplify the left-hand side of the equation by finding a common denominator.
4. Check your work by plugging the solution back into the original equation.

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

A: Here are some common mistakes to avoid when solving for $v$:

• Not isolating the variable $v$ on one side of the equation.
• Not using inverse operations to get rid of fractions and decimals.
• Not simplifying the left-hand side of the equation.
• Not checking your work by plugging the solution back into the original equation.

Q: How do I check my work when solving for $v$?

A: To check your work when solving for $v$, you need to plug the solution back into the original equation. If the solution is correct, the equation should be true. If the solution is incorrect, the equation will not be true.

Q: What are some real-world applications of solving for $v$?

A: Solving for $v$ has many real-world applications. For example, in physics, solving for velocity is crucial in understanding the motion of objects. In economics, solving for variables is essential in understanding the behavior of markets and making informed decisions.

Q: Can you provide some examples of solving for $v$?

A: Here are some examples of solving for $v$:

• Example 1: Solve for $v$ in the equation $2 = v + 3$.
• Example 2: Solve for $v$ in the equation $-4 = v - 2$.
• Example 3: Solve for $v$ in the equation $1 = v + \frac{1}{2}$.

Q: How do I simplify the left-hand side of the equation when solving for $v$?

A: To simplify the left-hand side of the equation when solving for $v$, you need to find a common denominator. This will help you combine the fractions and decimals on the left-hand side of the equation.

Q: What is the final answer to the equation $-5 = v - \frac{3}{4}$?

A: The final answer to the equation $-5 = v - \frac{3}{4}$ is $-\frac{17}{4}$.

Conclusion

In conclusion, solving for $v$ is an important concept in mathematics that involves isolating the variable $v$ on one side of an equation. By following the steps outlined in this article, you can solve for $v$ and simplify the left-hand side of the equation. Remember to always check your work by plugging the solution back into the original equation.