Select The Correct Answer.Solve The Equation For $x$ In Terms Of $c$.$\frac{2}{3}\left(c X+\frac{1}{2}\right)-\frac{1}{4}=\frac{5}{2}$A. $x=\frac{29}{8c}$ B. $x=\frac{29}{18c}$ C. $x=\frac{9}{4c}$

Introduction

Solving equations is a fundamental concept in mathematics that involves isolating the variable of interest. In this article, we will focus on solving a specific equation involving the variable $x$ in terms of $c$. We will use algebraic techniques to isolate $x$ and provide the correct solution.

The Equation

The given equation is:

$\frac{2}{3}\left(c x+\frac{1}{2}\right)-\frac{1}{4}=\frac{5}{2}$

Our goal is to solve for $x$ in terms of $c$.

Step 1: Simplify the Equation

To simplify the equation, we can start by multiplying both sides by 12, which is the least common multiple of 3 and 4.

$12\left(\frac{2}{3}\left(c x+\frac{1}{2}\right)-\frac{1}{4}\right)=12\left(\frac{5}{2}\right)$

This simplifies to:

$8\left(c x+\frac{1}{2}\right)-3=30$

Step 2: Distribute and Combine Like Terms

Next, we can distribute the 8 to the terms inside the parentheses and combine like terms.

$8cx+4-3=30$

This simplifies to:

$8cx+1=30$

Step 3: Isolate the Variable

To isolate the variable $x$, we can subtract 1 from both sides of the equation.

$8cx=30-1$

This simplifies to:

$8cx=29$

Step 4: Solve for $x$

Finally, we can solve for $x$ by dividing both sides of the equation by 8c.

$x=\frac{29}{8c}$

Conclusion

In this article, we solved the equation $\frac{2}{3}\left(c x+\frac{1}{2}\right)-\frac{1}{4}=\frac{5}{2}$ for $x$ in terms of $c$. We used algebraic techniques to simplify the equation, isolate the variable, and provide the correct solution.

Comparison of Solutions

Let's compare our solution with the given options:

A. $x=\frac{29}{8c}$ B. $x=\frac{29}{18c}$ C. $x=\frac{9}{4c}$

Our solution matches option A.

Discussion

Solving equations is an essential skill in mathematics that requires attention to detail and algebraic techniques. In this article, we demonstrated how to solve a specific equation involving the variable $x$ in terms of $c$. We hope that this article has provided a clear and concise guide to solving equations and has helped readers develop their problem-solving skills.

Additional Tips and Resources

For readers who want to practice solving equations, we recommend the following resources:

• Khan Academy: Algebra
• Mathway: Equation Solver
• Wolfram Alpha: Equation Solver

These resources provide interactive tools and examples to help readers practice solving equations and develop their problem-solving skills.

Final Thoughts

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Introduction

Solving equations is a fundamental concept in mathematics that involves isolating the variable of interest. In our previous article, we demonstrated how to solve a specific equation involving the variable $x$ in terms of $c$. In this article, we will address some frequently asked questions related to solving equations.

Q: What is the first step in solving an equation?

A: The first step in solving an equation is to simplify the equation by combining like terms and eliminating any parentheses.

Q: How do I isolate the variable in an equation?

A: To isolate the variable in an equation, you need to get the variable by itself 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 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, $2x+3=5$ is a linear equation. A quadratic equation, on the other hand, is an equation in which the highest power of the variable is 2. For example, $x^2+4x+4=0$ is a quadratic equation.

Q: How do I solve a quadratic equation?

A: To solve a quadratic equation, you can use the quadratic formula: $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$. Alternatively, you can factor the quadratic expression and solve for $x$.

Q: What is the order of operations in solving an equation?

A: The order of operations in solving an equation is:

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 check my solution to an equation?

A: To check your solution to an equation, you can plug the solution back into the original equation and verify that it is true.

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

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

• Not simplifying the equation before solving
• Not isolating the variable correctly
• Not checking the solution
• Not using the correct order of operations

Conclusion

Solving equations is a fundamental concept in mathematics that requires attention to detail and algebraic techniques. In this article, we addressed some frequently asked questions related to solving equations. We hope that this article has provided a clear and concise guide to solving equations and has helped readers develop their problem-solving skills.

Additional Tips and Resources

For readers who want to practice solving equations, we recommend the following resources:

• Khan Academy: Algebra
• Mathway: Equation Solver
• Wolfram Alpha: Equation Solver

These resources provide interactive tools and examples to help readers practice solving equations and develop their problem-solving skills.

Final Thoughts

Solving equations is a fundamental concept in mathematics that requires attention to detail and algebraic techniques. In this article, we addressed some frequently asked questions related to solving equations. We hope that this article has provided a clear and concise guide to solving equations and has helped readers develop their problem-solving skills.