An Equation Is Shown: 5 = \frac{1}{4}\left(\frac{1}{3} G - \frac{1}{2}\right ]What Is The Solution To The Equation? G = G = G =

Introduction

In this article, we will be solving an equation that involves a variable g. The equation is given as:

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

Our goal is to isolate the variable g and find its value.

Step 1: Multiply Both Sides by 4

To get rid of the fraction on the right-hand side, we can multiply both sides of the equation by 4.

$$20 = \frac{1}{3} g - \frac{1}{2}$$

Step 2: Add $\frac{1}{2}$ to Both Sides

Next, we can add $\frac{1}{2}$ to both sides of the equation to get rid of the fraction on the right-hand side.

$$20 + \frac{1}{2} = \frac{1}{3} g$$

Step 3: Simplify the Left-Hand Side

We can simplify the left-hand side of the equation by finding a common denominator for 20 and $\frac{1}{2}$.

$$\frac{40}{2} + \frac{1}{2} = \frac{1}{3} g$$

$$\frac{41}{2} = \frac{1}{3} g$$

Step 4: Multiply Both Sides by 3

To get rid of the fraction on the right-hand side, we can multiply both sides of the equation by 3.

$$\frac{41}{2} \cdot 3 = g$$

Step 5: Simplify the Left-Hand Side

We can simplify the left-hand side of the equation by multiplying $\frac{41}{2}$ by 3.

$$\frac{41 \cdot 3}{2} = g$$

$$\frac{123}{2} = g$$

Conclusion

We have successfully solved the equation for g and found its value to be $\frac{123}{2}$.

Final Answer

The final answer is $\boxed{\frac{123}{2}}$.

Explanation

To solve the equation, we used the following steps:

1. Multiply both sides by 4 to get rid of the fraction on the right-hand side.
2. Add $\frac{1}{2}$ to both sides to get rid of the fraction on the right-hand side.
3. Simplify the left-hand side by finding a common denominator for 20 and $\frac{1}{2}$.
4. Multiply both sides by 3 to get rid of the fraction on the right-hand side.
5. Simplify the left-hand side by multiplying $\frac{41}{2}$ by 3.

By following these steps, we were able to isolate the variable g and find its value.

Tips and Tricks

• When solving equations, it's often helpful to get rid of fractions by multiplying both sides by a common denominator.
• Be careful when adding or subtracting fractions to make sure you have a common denominator.
• Use the order of operations (PEMDAS) to simplify expressions and make it easier to solve equations.

Related Topics

• Solving linear equations
• Simplifying expressions
• Isolating variables

References

• Mathway
• Khan Academy
• Wolfram Alpha
  Frequently Asked Questions (FAQs) =====================================

Q: What is the equation given in the problem?

A: The equation given in the problem is:

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

Q: How do I solve the equation for g?

A: To solve the equation for g, you can follow the steps outlined in the article:

1. Multiply both sides by 4 to get rid of the fraction on the right-hand side.
2. Add $\frac{1}{2}$ to both sides to get rid of the fraction on the right-hand side.
3. Simplify the left-hand side by finding a common denominator for 20 and $\frac{1}{2}$.
4. Multiply both sides by 3 to get rid of the fraction on the right-hand side.
5. Simplify the left-hand side by multiplying $\frac{41}{2}$ by 3.

Q: What is the value of g?

A: The value of g is $\frac{123}{2}$.

Q: Can I use a calculator to solve the equation?

A: Yes, you can use a calculator to solve the equation. However, it's often helpful to understand the steps involved in solving the equation to ensure that you get the correct answer.

Q: What if I get stuck on a step?

A: If you get stuck on a step, try breaking it down into smaller parts or looking for a different way to approach the problem. You can also try using online resources such as Mathway or Khan Academy to get help.

Q: How do I simplify expressions?

A: To simplify expressions, you can use the order of operations (PEMDAS) to evaluate the expression from left to right. You can also try combining like terms or canceling out common factors.

Q: What is the order of operations?

A: The order of operations is:

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: Can I use a calculator to check my answer?

A: Yes, you can use a calculator to check your answer. However, it's often helpful to understand the steps involved in solving the equation to ensure that you get the correct answer.

Q: What if I make a mistake?

A: If you make a mistake, try going back to the previous step and re-evaluating your work. You can also try using online resources such as Mathway or Khan Academy to get help.

Q: How do I know if my answer is correct?

A: To check if your answer is correct, you can plug it back into the original equation and see if it's true. You can also try using online resources such as Mathway or Khan Academy to get help.

Q: Can I use this method to solve other equations?

A: Yes, you can use this method to solve other equations that involve variables and fractions. However, you may need to adjust the steps depending on the specific equation.

Q: What if I'm still having trouble?

A: If you're still having trouble, try seeking help from a teacher, tutor, or online resource such as Mathway or Khan Academy.