Solve For $w$.$42 = W + 6w$Simplify Your Answer As Much As Possible.$ W = W = W = [/tex]

Mar 10, 2025 by ADMIN 93 views

Solving for w in the Equation 42 = w + 6w

Introduction

In this article, we will delve into the world of algebra and solve for the variable w in the given equation 42 = w + 6w. This equation is a simple linear equation that can be solved using basic algebraic techniques. We will break down the solution step by step, making it easy to understand for readers of all levels.

Understanding the Equation

The given equation is 42 = w + 6w. To solve for w, we need to isolate the variable w on one side of the equation. The equation can be rewritten as 42 = 7w, where 7w is the sum of w and 6w.

Combining Like Terms

The next step is to combine like terms on the right-hand side of the equation. In this case, we have two terms with the variable w: w and 6w. We can combine these terms by adding their coefficients, which are 1 and 6, respectively. This gives us 7w.

Solving for w

Now that we have the equation 42 = 7w, we can solve for w by dividing both sides of the equation by 7. This will isolate the variable w on the left-hand side of the equation.

Step-by-Step Solution

To solve for w, we will follow these steps:

Divide both sides of the equation by 7: 42 ÷ 7 = 7w ÷ 7
Simplify the equation: 6 = w

Conclusion

In conclusion, we have solved for the variable w in the equation 42 = w + 6w. By combining like terms and isolating the variable w, we found that w = 6.

Final Answer

The final answer is w = 6.

Example Use Case

This equation can be used in a variety of real-world scenarios, such as:

Calculating the total cost of an item when the cost of the item and the cost of shipping are known.
Determining the amount of money that needs to be invested in a savings account to reach a certain goal.
Finding the value of a variable in a linear equation.

Tips and Tricks

When solving for a variable, make sure to isolate the variable on one side of the equation.
Use inverse operations to get rid of any coefficients or constants that are attached to the variable.
Check your work by plugging the solution back into the original equation.

Common Mistakes

Failing to combine like terms on the right-hand side of the equation.
Not isolating the variable on one side of the equation.
Not checking the solution by plugging it back into the original equation.

Real-World Applications

This equation has many real-world applications, such as:

Calculating the total cost of an item when the cost of the item and the cost of shipping are known.
Determining the amount of money that needs to be invested in a savings account to reach a certain goal.
Finding the value of a variable in a linear equation.

Conclusion

In conclusion, solving for w in the equation 42 = w + 6w is a simple process that involves combining like terms and isolating the variable w. By following the steps outlined in this article, readers can easily solve for w and apply the solution to real-world scenarios.

Introduction

In our previous article, we solved for the variable w in the equation 42 = w + 6w. In this article, we will answer some frequently asked questions about solving for w in this equation.

Q: What is the first step in solving for w in the equation 42 = w + 6w?

A: The first step in solving for w is to combine like terms on the right-hand side of the equation. In this case, we have two terms with the variable w: w and 6w. We can combine these terms by adding their coefficients, which are 1 and 6, respectively.

Q: How do I combine like terms on the right-hand side of the equation?

A: To combine like terms, you need to add the coefficients of the terms with the same variable. In this case, we have w and 6w, so we add their coefficients: 1 + 6 = 7. This gives us 7w.

Q: What is the next step in solving for w?

A: The next step in solving for w is to isolate the variable w on one side of the equation. We can do this by dividing both sides of the equation by 7.

Q: Why do I need to isolate the variable w on one side of the equation?

A: Isolating the variable w on one side of the equation allows us to find the value of w. If the variable w is not isolated, we will not be able to find its value.

Q: How do I check my solution?

A: To check your solution, you need to plug it back into the original equation. If the solution is correct, the equation will be true. If the solution is incorrect, the equation will not be true.

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

A: Some common mistakes to avoid when solving for w include:

Failing to combine like terms on the right-hand side of the equation.
Not isolating the variable w on one side of the equation.
Not checking the solution by plugging it back into the original equation.

Q: What are some real-world applications of solving for w in the equation 42 = w + 6w?

A: Some real-world applications of solving for w in the equation 42 = w + 6w include:

Calculating the total cost of an item when the cost of the item and the cost of shipping are known.
Determining the amount of money that needs to be invested in a savings account to reach a certain goal.
Finding the value of a variable in a linear equation.

Q: Can I use this equation to solve for w in other equations?

A: Yes, you can use this equation to solve for w in other equations. However, you need to make sure that the equation is in the same form as the original equation.

Q: How do I know if the equation is in the same form as the original equation?

A: To determine if the equation is in the same form as the original equation, you need to check if the coefficients of the terms with the same variable are the same. If they are the same, the equation is in the same form as the original equation.

Q: What if I get stuck while solving for w?

A: If you get stuck while solving for w, you can try the following:

Read the problem carefully and make sure you understand what is being asked.
Break down the problem into smaller steps and solve each step separately.
Ask for help from a teacher or a tutor.