Solve For $w$.$\frac{w}{2} - \frac{3w}{4} = \frac{w}{8}$Simplify Your Answer As Much As Possible.$w =$

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Introduction

In mathematics, solving equations is a fundamental concept that helps us find the value of unknown variables. In this article, we will focus on solving a linear equation involving a variable $w$. The given equation is $\frac{w}{2} - \frac{3w}{4} = \frac{w}{8}$, and our goal is to simplify it and find the value of $w$.

Understanding the Equation

Before we start solving the equation, let's understand its components. The equation is a linear equation, which means it is an equation in which the highest power of the variable is 1. In this case, the variable is $w$, and the equation is $\frac{w}{2} - \frac{3w}{4} = \frac{w}{8}$.

Step 1: Multiply Both Sides by the Least Common Multiple (LCM)

To simplify the equation, we need to get rid of the fractions. The least common multiple (LCM) of 2, 4, and 8 is 8. We can multiply both sides of the equation by 8 to eliminate the fractions.

$\frac{w}{2} \cdot 8 - \frac{3w}{4} \cdot 8 = \frac{w}{8} \cdot 8$

This simplifies to:

$4w - 6w = w$

Step 2: Combine Like Terms

Now that we have eliminated the fractions, we can combine like terms. In this case, we have two terms with the variable $w$: $4w$ and $-6w$. We can combine these terms by adding or subtracting their coefficients.

$4w - 6w = -2w$

So, the equation becomes:

$-2w = w$

Step 3: Add $2w$ to Both Sides

To isolate the variable $w$, we need to get rid of the negative term on the left side of the equation. We can do this by adding $2w$ to both sides of the equation.

$-2w + 2w = w + 2w$

This simplifies to:

$0 = 3w$

Step 4: Divide Both Sides by 3

Now that we have isolated the variable $w$, we can divide both sides of the equation by 3 to find the value of $w$.

$\frac{0}{3} = \frac{3w}{3}$

This simplifies to:

$0 = w$

Conclusion

In this article, we have solved the equation $\frac{w}{2} - \frac{3w}{4} = \frac{w}{8}$ and found the value of $w$. By following the steps outlined above, we have simplified the equation and isolated the variable $w$. The final answer is $w = 0$.

Final Answer

The final answer is $\boxed{0}$.

Frequently Asked Questions

• Q: What is the value of $w$ in the equation $\frac{w}{2} - \frac{3w}{4} = \frac{w}{8}$? A: The value of $w$ is 0.
• Q: How do I simplify the equation $\frac{w}{2} - \frac{3w}{4} = \frac{w}{8}$? A: To simplify the equation, you can multiply both sides by the least common multiple (LCM) of 2, 4, and 8, which is 8. Then, you can combine like terms and isolate the variable $w$.
• Q: What is the least common multiple (LCM) of 2, 4, and 8? A: The least common multiple (LCM) of 2, 4, and 8 is 8.
  

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Introduction

In our previous article, we solved the equation $\frac{w}{2} - \frac{3w}{4} = \frac{w}{8}$ and found the value of $w$ to be 0. However, we understand that sometimes, you may have questions or need further clarification on the steps involved in solving the equation. In this article, we will provide a Q&A guide to help you better understand the process of simplifying the equation and solving for $w$.

Q&A Guide

Q: What is the first step in solving the equation $\frac{w}{2} - \frac{3w}{4} = \frac{w}{8}$?

A: The first step in solving the equation is to multiply both sides by the least common multiple (LCM) of 2, 4, and 8, which is 8. This will eliminate the fractions and make it easier to combine like terms.

Q: Why do we need to multiply both sides by the LCM?

A: We need to multiply both sides by the LCM to eliminate the fractions. This is because the LCM is the smallest number that all the denominators (2, 4, and 8) can divide into evenly.

Q: What is the next step after multiplying both sides by the LCM?

A: After multiplying both sides by the LCM, we need to combine like terms. In this case, we have two terms with the variable $w$: $4w$ and $-6w$. We can combine these terms by adding or subtracting their coefficients.

Q: How do we combine like terms?

A: To combine like terms, we add or subtract the coefficients of the terms with the same variable. In this case, we have $4w$ and $-6w$, so we can combine them by subtracting their coefficients: $4w - 6w = -2w$.

Q: What is the final step in solving the equation?

A: The final step in solving the equation is to isolate the variable $w$. In this case, we have the equation $-2w = w$, and we can isolate $w$ by adding $2w$ to both sides of the equation.

Q: Why do we need to add $2w$ to both sides of the equation?

A: We need to add $2w$ to both sides of the equation to isolate the variable $w$. This is because we want to get $w$ by itself on one side of the equation.

Q: What is the final answer to the equation $\frac{w}{2} - \frac{3w}{4} = \frac{w}{8}$?

A: The final answer to the equation is $w = 0$.

Common Mistakes to Avoid

• Not multiplying both sides by the LCM: Failing to multiply both sides by the LCM can lead to incorrect solutions.
• Not combining like terms: Failing to combine like terms can lead to incorrect solutions.
• Not isolating the variable: Failing to isolate the variable can lead to incorrect solutions.

Tips and Tricks

• Use the LCM to eliminate fractions: Multiplying both sides by the LCM can make it easier to combine like terms and isolate the variable.
• Combine like terms carefully: Make sure to combine like terms correctly to avoid incorrect solutions.
• Isolate the variable carefully: Make sure to isolate the variable correctly to avoid incorrect solutions.

Conclusion

In this article, we have provided a Q&A guide to help you better understand the process of simplifying the equation and solving for $w$. By following the steps outlined in this article, you should be able to solve the equation $\frac{w}{2} - \frac{3w}{4} = \frac{w}{8}$ and find the value of $w$.

Final Answer

The final answer is $\boxed{0}$.