Solve For $w$.$3(w-3) = 2w + 3 - 3(-5w - 2)$Simplify Your Answer As Much As Possible.$ W = W = W = [/tex]

Introduction

In this article, we will delve into the world of algebra and solve for the variable w in a given equation. The equation is a linear equation, and we will use various algebraic techniques to simplify and solve for w. We will break down the solution into manageable steps, making it easy to follow and understand.

The Equation

The given equation is:

$$3(w-3) = 2w + 3 - 3(-5w - 2)$$

Our goal is to solve for w, which means we need to isolate the variable w on one side of the equation.

Step 1: Distribute the Numbers

To start solving the equation, we need to distribute the numbers inside the parentheses. We will start with the left side of the equation:

$$3(w-3) = 3w - 9$$

Now, let's distribute the numbers on the right side of the equation:

$$2w + 3 - 3(-5w - 2) = 2w + 3 + 15w + 6$$

Simplifying the right side of the equation, we get:

$$2w + 3 + 15w + 6 = 17w + 9$$

Step 2: Combine Like Terms

Now that we have distributed the numbers, we can combine like terms on both sides of the equation. On the left side, we have:

$$3w - 9$$

On the right side, we have:

$$17w + 9$$

We can combine the like terms on the right side by adding the coefficients of w:

$$17w + 9 = 17w + 9$$

Step 3: Isolate the Variable w

Now that we have combined like terms, we can isolate the variable w on one side of the equation. We will start by subtracting 17w from both sides of the equation:

$$3w - 9 = 17w + 9 - 17w$$

Simplifying the right side of the equation, we get:

$$3w - 9 = 9$$

Next, we will add 9 to both sides of the equation:

$$3w - 9 + 9 = 9 + 9$$

Simplifying the right side of the equation, we get:

$$3w = 18$$

Step 4: Solve for w

Finally, we can solve for w by dividing both sides of the equation by 3:

$$\frac{3w}{3} = \frac{18}{3}$$

Simplifying the equation, we get:

$$w = 6$$

Conclusion

In this article, we solved for the variable w in a given equation. We used various algebraic techniques, including distributing numbers, combining like terms, and isolating the variable w. By following these steps, we were able to simplify the equation and solve for w. The final solution is:

$$w = 6$$

Tips and Tricks

• When solving equations, it's essential to follow the order of operations (PEMDAS).
• Distributing numbers inside parentheses can help simplify the equation.
• Combining like terms can help isolate the variable w.
• Isolating the variable w on one side of the equation is crucial to solving the equation.

Common Mistakes

• Failing to distribute numbers inside parentheses can lead to incorrect solutions.
• Not combining like terms can make it difficult to isolate the variable w.
• Not following the order of operations (PEMDAS) can result in incorrect solutions.

Real-World Applications

Solving equations is a fundamental skill in mathematics and has numerous real-world applications. For example:

• In physics, equations are used to describe the motion of objects and predict their behavior.
• In economics, equations are used to model the behavior of markets and predict economic trends.
• In computer science, equations are used to solve problems in fields such as machine learning and data analysis.

Conclusion

Introduction

In our previous article, we solved for the variable w in a given equation. In this article, we will provide a Q&A guide to help you better understand the solution and address any questions you may have.

Q: What is the equation we solved for w?

A: The equation we solved for w is:

$$3(w-3) = 2w + 3 - 3(-5w - 2)$$

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

A: The first step in solving the equation is to distribute the numbers inside the parentheses. We start with the left side of the equation:

$$3(w-3) = 3w - 9$$

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

A: The next step in solving the equation is to combine like terms on both sides of the equation. On the left side, we have:

$$3w - 9$$

On the right side, we have:

$$17w + 9$$

We can combine the like terms on the right side by adding the coefficients of w:

$$17w + 9 = 17w + 9$$

Q: How do we isolate the variable w?

A: To isolate the variable w, we need to get w on one side of the equation by itself. We can do this by subtracting 17w from both sides of the equation:

$$3w - 9 = 17w + 9 - 17w$$

Simplifying the right side of the equation, we get:

$$3w - 9 = 9$$

Next, we will add 9 to both sides of the equation:

$$3w - 9 + 9 = 9 + 9$$

Simplifying the right side of the equation, we get:

$$3w = 18$$

Q: How do we solve for w?

A: To solve for w, we need to get w by itself on one side of the equation. We can do this by dividing both sides of the equation by 3:

$$\frac{3w}{3} = \frac{18}{3}$$

Simplifying the equation, we get:

$$w = 6$$

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

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

• Failing to distribute numbers inside parentheses
• Not combining like terms
• Not following the order of operations (PEMDAS)
• Not isolating the variable w on one side of the equation

Q: What are some real-world applications of solving equations?

A: Solving equations has numerous real-world applications, including:

• In physics, equations are used to describe the motion of objects and predict their behavior.
• In economics, equations are used to model the behavior of markets and predict economic trends.
• In computer science, equations are used to solve problems in fields such as machine learning and data analysis.

Q: How can I practice solving equations?

A: You can practice solving equations by:

• Working through example problems
• Using online resources and practice exercises
• Creating your own problems and solving them
• Joining a study group or working with a tutor

Conclusion

Solving equations is a critical skill in mathematics and has numerous real-world applications. By following the steps outlined in this article and avoiding common mistakes, you can become proficient in solving equations and apply your skills to real-world problems. Remember to practice regularly and seek help when needed to improve your skills.