Solve For $w$.1. $5w + 9z = 2z + 3w$Choose The Correct Solution For $w$:A. $w = -\frac{7}{2}z$B. $w = -\frac{2}{7}z$C. $w = -2z$D. $w = -7z$

Introduction

Linear equations are a fundamental concept in mathematics, and solving them is a crucial skill for students to master. In this article, we will focus on solving a specific type of linear equation, where we need to isolate a variable, in this case, $w$. We will use a step-by-step approach to solve the equation and provide a clear explanation of each step.

The Equation

The given equation is:

$$5w + 9z = 2z + 3w$$

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

Step 1: Simplify the Equation

To simplify the equation, we can start by combining like terms. We can subtract $3w$ from both sides of the equation to get:

$$2w + 9z = 2z$$

This simplifies the equation and makes it easier to work with.

Step 2: Isolate the Variable

Next, we need to isolate the variable $w$. We can do this by subtracting $9z$ from both sides of the equation:

$$2w = 2z - 9z$$

This simplifies the equation further and isolates the variable $w$.

Step 3: Solve for $w$

Now that we have isolated the variable $w$, we can solve for it. We can start by combining the like terms on the right-hand side of the equation:

$$2w = -7z$$

Next, we can divide both sides of the equation by 2 to solve for $w$:

$$w = -\frac{7}{2}z$$

Conclusion

In this article, we solved a linear equation to isolate the variable $w$. We used a step-by-step approach to simplify the equation, isolate the variable, and solve for $w$. The correct solution for $w$ is:

$$w = -\frac{7}{2}z$$

This solution is the correct answer among the options provided.

Discussion

The equation we solved is a linear equation, which means it can be represented graphically as a straight line. The solution we obtained is a linear function of $z$, which means it can be represented graphically as a straight line.

Solving Linear Equations: Tips and Tricks

Here are some tips and tricks to help you solve linear equations:

• Combine like terms: Combine like terms on both sides of the equation to simplify it.
• Isolate the variable: Isolate the variable on one side of the equation to solve for it.
• Use inverse operations: Use inverse operations to solve for the variable.
• Check your solution: Check your solution by plugging it back into the original equation.

By following these tips and tricks, you can become proficient in solving linear equations and apply them to real-world problems.

Real-World Applications

Linear equations have many real-world applications, including:

• Physics: Linear equations are used to describe the motion of objects.
• Engineering: Linear equations are used to design and optimize systems.
• Economics: Linear equations are used to model economic systems and make predictions.

By understanding how to solve linear equations, you can apply them to real-world problems and make informed decisions.

Conclusion

In this article, we solved a linear equation to isolate the variable $w$. We used a step-by-step approach to simplify the equation, isolate the variable, and solve for $w$. The correct solution for $w$ is:

$$w = -\frac{7}{2}z$$

Introduction

In our previous article, we solved a linear equation to isolate the variable $w$. We used a step-by-step approach to simplify the equation, isolate the variable, and solve for $w$. In this article, we will provide a Q&A guide to help you understand how to solve linear equations.

Q: What is a linear equation?

A: A linear equation is an equation in which the highest power of the variable(s) is 1. It can be represented graphically as a straight line.

Q: How do I simplify a linear equation?

A: To simplify a linear equation, you can combine like terms on both sides of the equation. This will make it easier to work with and isolate the variable.

Q: How do I isolate the variable in a linear equation?

A: To isolate the variable in a linear equation, you can use inverse operations to get the variable on one side of the equation. For example, if you have the equation $2x + 3 = 5$, you can subtract 3 from both sides to get $2x = 2$, and then divide both sides by 2 to get $x = 1$.

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(s) is 1, while a quadratic equation is an equation in which the highest power of the variable(s) is 2. For example, the equation $x + 2 = 3$ is a linear equation, while the equation $x^2 + 2x + 1 = 0$ is a quadratic equation.

Q: How do I solve a linear equation with multiple variables?

A: To solve a linear equation with multiple variables, you can use the same steps as you would for a linear equation with one variable. However, you will need to isolate each variable separately. For example, if you have the equation $2x + 3y = 5$, you can isolate $x$ by subtracting $3y$ from both sides to get $2x = 5 - 3y$, and then divide both sides by 2 to get $x = \frac{5 - 3y}{2}$.

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

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

• Not combining like terms: Failing to combine like terms on both sides of the equation can make it difficult to isolate the variable.
• Not using inverse operations: Failing to use inverse operations to get the variable on one side of the equation can make it difficult to solve the equation.
• Not checking your solution: Failing to check your solution by plugging it back into the original equation can lead to incorrect answers.

Q: How do I check my solution to a linear equation?

A: To check your solution to a linear equation, you can plug it back into the original equation and see if it is true. For example, if you have the equation $x + 2 = 3$ and you solve for $x$ to get $x = 1$, you can plug $x = 1$ back into the original equation to get $1 + 2 = 3$, which is true.

Conclusion

In this article, we provided a Q&A guide to help you understand how to solve linear equations. We covered topics such as simplifying linear equations, isolating variables, and checking solutions. By following these tips and tricks, you can become proficient in solving linear equations and apply them to real-world problems.

Real-World Applications

Linear equations have many real-world applications, including:

• Physics: Linear equations are used to describe the motion of objects.
• Engineering: Linear equations are used to design and optimize systems.
• Economics: Linear equations are used to model economic systems and make predictions.

By understanding how to solve linear equations, you can apply them to real-world problems and make informed decisions.

Practice Problems

Here are some practice problems to help you practice solving linear equations:

1. Solve the equation $2x + 3 = 5$ for $x$.
2. Solve the equation $x + 2y = 3$ for $x$.
3. Solve the equation $2x - 3y = 5$ for $x$.

Answer Key

1. $x = 1$
2. $x = 3 - 2y$
3. $x = \frac{5 + 3y}{2}$