Select The Correct Answer.Which Equation Is Correctly Rewritten To Solve For X X X ? − F X − G = H -f X - G = H − F X − G = H A. X = H + G F X = \frac{h+g}{f} X = F H + G ​ B. X = G − H − F X = \frac{g-h}{-f} X = − F G − H ​ C. X = H − G − F X = \frac{h-g}{-f} X = − F H − G ​ D. X = H + G − F X = \frac{h+g}{-f} X = − F H + G ​

Introduction

Solving linear equations is a fundamental concept in mathematics, and it's essential to understand how to rewrite equations to solve for a specific variable. In this article, we'll focus on solving for $x$ in the equation $-f x - g = h$. We'll explore the correct method to rewrite the equation and provide step-by-step examples to help you understand the concept.

Understanding the Equation

The given equation is $-f x - g = h$. Our goal is to solve for $x$, which means we need to isolate the variable $x$ on one side of the equation. To do this, we'll use algebraic manipulations to rewrite the equation in a more manageable form.

Rewriting the Equation

To solve for $x$, we need to get rid of the negative sign in front of the $f x$ term. We can do this by multiplying both sides of the equation by $-1$. This will change the sign of the $f x$ term, but it will also change the sign of the $h$ term.

-f x - g = h
\Rightarrow f x + g = -h

Now, we can add $g$ to both sides of the equation to get rid of the $-g$ term.

f x + g = -h
\Rightarrow f x = -h - g

Solving for $x$

Now that we have the equation in the form $f x = -h - g$, we can solve for $x$ by dividing both sides of the equation by $f$.

f x = -h - g
\Rightarrow x = \frac{-h - g}{f}

However, we can simplify the expression by combining the terms in the numerator.

x = \frac{-h - g}{f}
\Rightarrow x = \frac{h + g}{-f}

Conclusion

In this article, we've learned how to rewrite the equation $-f x - g = h$ to solve for $x$. We used algebraic manipulations to isolate the variable $x$ on one side of the equation. By following the steps outlined in this article, you should be able to solve for $x$ in similar equations.

Answer

The correct answer is:

• D. $x = \frac{h+g}{-f}$

This is the correct solution to the equation $-f x - g = h$. By following the steps outlined in this article, you should be able to verify that this is the correct solution.

Practice Problems

To reinforce your understanding of solving linear equations, try the following practice problems:

1. Solve for $x$ in the equation $2x + 3 = 5$.
2. Solve for $y$ in the equation $y - 2 = 3$.
3. Solve for $z$ in the equation $z + 1 = -2$.

By practicing these problems, you'll become more comfortable with solving linear equations and be able to apply this skill to a wide range of mathematical problems.

Additional Resources

If you're looking for additional resources to help you learn more about solving linear equations, check out the following:

• Khan Academy: Solving Linear Equations
• Mathway: Solving Linear Equations
• IXL: Solving Linear Equations

These resources provide interactive lessons, examples, and practice problems to help you learn more about solving linear equations.

Final Thoughts

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Q: What is a linear equation?

A: A linear equation is an equation in which the highest power of the variable(s) is 1. In other words, it's an equation that can be written in the form ax + b = c, where a, b, and c are constants.

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. This can be done by adding, subtracting, multiplying, or dividing both sides of the equation by the same value.

Q: What is the order of operations when solving a linear equation?

A: When solving a linear equation, you should follow the order of operations (PEMDAS):

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

Q: How do I isolate the variable in a linear equation?

A: To isolate the variable in a linear equation, you can use the following steps:

1. Add or subtract the same value to both sides of the equation to get rid of any constants on the same side as the variable.
2. Multiply or divide both sides of the equation by the same value to get rid of any coefficients on the same side as the variable.

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, while a quadratic equation is an equation in which the highest power of the variable(s) is 2.

Q: How do I solve a quadratic equation?

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

x = (-b ± √(b^2 - 4ac)) / 2a

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

Q: What is the significance of solving linear equations?

A: Solving linear equations is an essential skill in mathematics, as it allows you to:

• Solve real-world problems that involve variables and constants.
• Understand the relationships between variables and constants.
• Make predictions and forecasts based on data.

Q: How can I practice solving linear equations?

A: You can practice solving linear equations by:

• Working through example problems in a textbook or online resource.
• Using online tools or apps to generate practice problems.
• Creating your own practice problems based on real-world scenarios.

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

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

• Forgetting to follow the order of operations.
• Not isolating the variable on one side of the equation.
• Making errors when adding, subtracting, multiplying, or dividing both sides of the equation.

Q: How can I improve my skills in solving linear equations?

A: To improve your skills in solving linear equations, you can:

• Practice regularly to build your confidence and fluency.
• Seek help from a teacher, tutor, or online resource if you're struggling.
• Apply your skills to real-world problems to see the relevance and importance of solving linear equations.

Conclusion

Solving linear equations is an essential skill in mathematics, and it's used to solve real-world problems that involve variables and constants. By following the steps outlined in this article, you should be able to solve linear equations with confidence. Remember to practice regularly and seek help if you're struggling.