Solve For $v$.$-2.9 = \frac{v}{4}$

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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 the variable $v$ in the equation $-2.9 = \frac{v}{4}$. This equation is a simple linear equation that can be solved using basic algebraic techniques.

Understanding the Equation

The given equation is $-2.9 = \frac{v}{4}$. This equation states that the value of $-2.9$ is equal to the value of $v$ divided by $4$. To solve for $v$, we need to isolate the variable $v$ on one side of the equation.

Step 1: Multiply Both Sides by 4

To isolate the variable $v$, we can start by multiplying both sides of the equation by $4$. This will eliminate the fraction on the right-hand side of the equation.

-2.9 = \frac{v}{4}

Multiplying both sides by $4$ gives us:

-2.9 \times 4 = v

This simplifies to:

-11.6 = v

Step 2: Simplify the Equation

Now that we have isolated the variable $v$, we can simplify the equation by evaluating the expression on the left-hand side.

-11.6 = v

This equation states that the value of $v$ is equal to $-11.6$.

Conclusion

In this article, we solved for the variable $v$ in the equation $-2.9 = \frac{v}{4}$. We used basic algebraic techniques to isolate the variable $v$ on one side of the equation. The final solution is $v = -11.6$.

Tips and Tricks

When solving for a variable, it's essential to follow the order of operations (PEMDAS) and to simplify the equation as much as possible. Additionally, make sure to check your work by plugging the solution back into the original equation.

Real-World Applications

Solving for a variable is a fundamental concept in mathematics that has numerous real-world applications. For example, in physics, solving for a variable can help us understand the motion of objects and the forces acting upon them. In engineering, solving for a variable can help us design and optimize systems.

Common Mistakes

When solving for a variable, it's easy to make mistakes. Some common mistakes include:

• Not following the order of operations (PEMDAS)
• Not simplifying the equation
• Not checking the solution by plugging it back into the original equation

Conclusion

In conclusion, solving for a variable is a fundamental concept in mathematics that involves isolating the variable on one side of the equation. By following basic algebraic techniques and simplifying the equation, we can solve for the variable $v$ in the equation $-2.9 = \frac{v}{4}$. The final solution is $v = -11.6$.

Additional Resources

For more information on solving for a variable, check out the following resources:

• Khan Academy: Solving Linear Equations
• Mathway: Solving Linear Equations
• Wolfram Alpha: Solving Linear Equations

Final Thoughts

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Introduction

In our previous article, we solved for the variable $v$ in the equation $-2.9 = \frac{v}{4}$. In this article, we will answer some frequently asked questions (FAQs) related to solving for a variable.

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

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

A: To simplify an equation, we need to combine like terms and eliminate any fractions or decimals. We can do this by multiplying both sides of the equation by a common factor or by using algebraic properties such as the distributive property.

Q: What is the distributive property?

A: The distributive property is a mathematical property that allows us to multiply a single term by multiple terms. It states that:

a(b + c) = ab + ac

Q: How do I check my work?

A: To check your work, plug the solution back into the original equation and see if it is true. 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 common mistakes to avoid when solving for a variable?

A: Some common mistakes to avoid when solving for a variable include:

• Not following the order of operations (PEMDAS)
• Not simplifying the equation
• Not checking the solution by plugging it back into the original equation
• Not using algebraic properties such as the distributive property

Q: How do I use algebraic properties to simplify an equation?

A: Algebraic properties such as the distributive property can be used to simplify an equation by allowing us to multiply a single term by multiple terms. For example:

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 is 1. For example:

2x + 3 = 0

A quadratic equation is an equation in which the highest power of the variable is 2. For example:

x^2 + 4x + 4 = 0

Q: How do I solve a quadratic equation?

A: To solve a quadratic equation, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

where a, b, and c are the coefficients of the quadratic equation.

Conclusion

In this article, we answered some frequently asked questions (FAQs) related to solving for a variable. We covered topics such as the order of operations (PEMDAS), simplifying an equation, and using algebraic properties to simplify an equation. We also discussed common mistakes to avoid when solving for a variable and how to solve a quadratic equation.

Additional Resources

For more information on solving for a variable, check out the following resources:

• Khan Academy: Solving Linear Equations
• Mathway: Solving Linear Equations
• Wolfram Alpha: Solving Linear Equations

Final Thoughts

Solving for a variable is a fundamental concept in mathematics that has numerous real-world applications. By following basic algebraic techniques and simplifying the equation, we can solve for the variable $v$ in the equation $-2.9 = \frac{v}{4}$. The final solution is $v = -11.6$.