Solve For $v$.$4v + 17 = 85$Simplify Your Answer As Much As Possible.$v =$

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Introduction

Solving for a variable in an algebraic equation is a fundamental concept in mathematics. In this article, we will focus on solving for the variable $v$ in the equation $4v + 17 = 85$. This equation is a linear equation, and we will use the method of subtraction and division to isolate the variable $v$.

Understanding the Equation

The given equation is $4v + 17 = 85$. This equation states that the product of $4$ and $v$ plus $17$ is equal to $85$. To solve for $v$, we need to isolate the variable $v$ on one side of the equation.

Step 1: Subtract 17 from Both Sides

To isolate the term with the variable $v$, we need to subtract $17$ from both sides of the equation. This will give us:

$$4v + 17 - 17 = 85 - 17$$

Simplifying the equation, we get:

$$4v = 68$$

Step 2: Divide Both Sides by 4

Now that we have isolated the term with the variable $v$, we need to divide both sides of the equation by $4$ to solve for $v$. This will give us:

$$\frac{4v}{4} = \frac{68}{4}$$

Simplifying the equation, we get:

$$v = 17$$

Conclusion

In this article, we solved for the variable $v$ in the equation $4v + 17 = 85$. We used the method of subtraction and division to isolate the variable $v$ and found that $v = 17$.

Final Answer

The final answer to the equation $4v + 17 = 85$ is:

$v = 17$

Related Topics

• Solving linear equations
• Isolating variables
• Algebraic manipulations

Example Problems

• Solve for $x$: $2x + 5 = 11$
• Solve for $y$: $3y - 2 = 7$
• Solve for $z$: $z + 4 = 9$

Tips and Tricks

• When solving for a variable, always isolate the variable on one side of the equation.
• Use the order of operations (PEMDAS) to simplify the equation.
• Check your answer by plugging it back into the original equation.

Common Mistakes

• Forgetting to isolate the variable on one side of the equation.
• Not simplifying the equation before solving for the variable.
• Not checking the answer by plugging it back into the original equation.

Real-World Applications

• Solving for a variable in an algebraic equation is a fundamental concept in mathematics and has many real-world applications, such as:
  • Physics: Solving for velocity and acceleration in motion problems.
  • Engineering: Solving for stress and strain in materials science.
  • Economics: Solving for supply and demand in market equilibrium problems.

Further Reading

• For more information on solving linear equations, see the article "Solving Linear Equations: A Step-by-Step Guide".
• For more information on isolating variables, see the article "Isolating Variables: A Guide to Algebraic Manipulations".
• For more information on algebraic manipulations, see the article "Algebraic Manipulations: A Guide to Simplifying Equations".
  

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Introduction

In our previous article, we solved for the variable $v$ in the equation $4v + 17 = 85$. In this article, we will answer some frequently asked questions related to solving for $v$ in this equation.

Q&A

Q: What is the first step in solving for $v$ in the equation $4v + 17 = 85$?

A: The first step in solving for $v$ in the equation $4v + 17 = 85$ is to subtract $17$ from both sides of the equation. This will give us $4v = 68$.

Q: Why do we need to subtract $17$ from both sides of the equation?

A: We need to subtract $17$ from both sides of the equation to isolate the term with the variable $v$. By subtracting $17$ from both sides, we are essentially removing the constant term from the equation, which allows us to focus on solving for the variable $v$.

Q: What is the next step in solving for $v$ in the equation $4v + 17 = 85$?

A: The next step in solving for $v$ in the equation $4v + 17 = 85$ is to divide both sides of the equation by $4$. This will give us $v = 17$.

Q: Why do we need to divide both sides of the equation by $4$?

A: We need to divide both sides of the equation by $4$ to solve for the variable $v$. By dividing both sides by $4$, we are essentially isolating the variable $v$ and finding its value.

Q: What is the final answer to the equation $4v + 17 = 85$?

A: The final answer to the equation $4v + 17 = 85$ is $v = 17$.

Q: Can I use a calculator to solve for $v$ in the equation $4v + 17 = 85$?

A: Yes, you can use a calculator to solve for $v$ in the equation $4v + 17 = 85$. However, it's always a good idea to show your work and follow the steps outlined above to ensure that you understand the solution.

Q: What if I get a different answer when using a calculator?

A: If you get a different answer when using a calculator, it's possible that there was an error in your calculation. Double-check your work and make sure that you followed the steps outlined above.

Q: Can I use this method to solve for $v$ in other equations?

A: Yes, you can use this method to solve for $v$ in other equations. The steps outlined above are general and can be applied to any linear equation.

Related Topics

• Solving linear equations
• Isolating variables
• Algebraic manipulations

Example Problems

• Solve for $x$: $2x + 5 = 11$
• Solve for $y$: $3y - 2 = 7$
• Solve for $z$: $z + 4 = 9$

Tips and Tricks

• When solving for a variable, always isolate the variable on one side of the equation.
• Use the order of operations (PEMDAS) to simplify the equation.
• Check your answer by plugging it back into the original equation.

Common Mistakes

• Forgetting to isolate the variable on one side of the equation.
• Not simplifying the equation before solving for the variable.
• Not checking the answer by plugging it back into the original equation.

Real-World Applications

• Solving for a variable in an algebraic equation is a fundamental concept in mathematics and has many real-world applications, such as:
  • Physics: Solving for velocity and acceleration in motion problems.
  • Engineering: Solving for stress and strain in materials science.
  • Economics: Solving for supply and demand in market equilibrium problems.

Further Reading

• For more information on solving linear equations, see the article "Solving Linear Equations: A Step-by-Step Guide".
• For more information on isolating variables, see the article "Isolating Variables: A Guide to Algebraic Manipulations".
• For more information on algebraic manipulations, see the article "Algebraic Manipulations: A Guide to Simplifying Equations".