Generate A Plan And Describe The Steps Needed To Solve The Equation.$34 = -(m + 3$\]

Introduction

In mathematics, solving equations is a fundamental concept that helps us understand the relationships between variables. In this article, we will focus on solving the equation $34 = -(m + 3)$. This equation involves a negative sign, parentheses, and a variable, making it a bit more challenging to solve. Our goal is to generate a plan and describe the steps needed to solve this equation.

Understanding the Equation

Before we dive into solving the equation, let's break it down and understand what it means. The equation is $34 = -(m + 3)$. Here, we have a negative sign in front of the parentheses, which means that the expression inside the parentheses will be negated. The variable $m$ is inside the parentheses, and we are asked to find its value.

Step 1: Distribute the Negative Sign

The first step in solving this equation is to distribute the negative sign to the expression inside the parentheses. This means that we will multiply the negative sign by each term inside the parentheses. In this case, we have $-(m + 3)$, which can be rewritten as $-m - 3$.

# Distributing the negative sign
equation = 34
negative_sign = -1
parentheses = m + 3
distributed_equation = negative_sign * parentheses
print(distributed_equation)  # Output: -m - 3

Step 2: Simplify the Equation

Now that we have distributed the negative sign, we can simplify the equation by combining like terms. In this case, we have $-m - 3 = 34$. We can add $m$ to both sides of the equation to get rid of the negative sign.

# Simplifying the equation
simplified_equation = -m - 3 + m
print(simplified_equation)  # Output: -3

Step 3: Add 3 to Both Sides

The next step is to add 3 to both sides of the equation to isolate the variable $m$. This will give us $-3 + 3 = m$.

# Adding 3 to both sides
added_equation = -3 + 3
print(added_equation)  # Output: 0

Step 4: Solve for m

Finally, we can solve for $m$ by setting the equation equal to 0. This gives us $m = 0$.

# Solving for m
m = 0
print(m)  # Output: 0

Conclusion

In this article, we generated a plan and described the steps needed to solve the equation $34 = -(m + 3)$. We distributed the negative sign, simplified the equation, added 3 to both sides, and finally solved for $m$. The final answer is $m = 0$. This equation is a great example of how to solve equations involving negative signs and parentheses.

Tips and Variations

• When solving equations involving negative signs, make sure to distribute the negative sign to each term inside the parentheses.
• When simplifying equations, combine like terms to make the equation easier to solve.
• When adding or subtracting numbers, make sure to add or subtract the same value to both sides of the equation.

Common Mistakes

• Failing to distribute the negative sign to each term inside the parentheses.
• Not combining like terms when simplifying the equation.
• Adding or subtracting different values to both sides of the equation.

Real-World Applications

Solving equations involving negative signs and parentheses is a fundamental concept in mathematics that has many real-world applications. For example, in physics, we use equations to describe the motion of objects. In economics, we use equations to model the behavior of markets. In computer science, we use equations to optimize algorithms.

Final Thoughts

Q: What is the first step in solving an equation involving a negative sign and parentheses?

A: The first step in solving an equation involving a negative sign and parentheses is to distribute the negative sign to each term inside the parentheses. This means that you will multiply the negative sign by each term inside the parentheses.

Q: How do I distribute the negative sign to each term inside the parentheses?

A: To distribute the negative sign to each term inside the parentheses, you can use the following steps:

1. Multiply the negative sign by each term inside the parentheses.
2. Write the result as a single expression.

For example, if you have the equation $-(m + 3)$, you would distribute the negative sign as follows:

$-(m + 3) = -m - 3$

Q: What is the next step in solving an equation involving a negative sign and parentheses?

A: The next step in solving an equation involving a negative sign and parentheses is to simplify the equation by combining like terms. This means that you will add or subtract the same value to both sides of the equation.

Q: How do I simplify the equation by combining like terms?

A: To simplify the equation by combining like terms, you can use the following steps:

1. Identify the like terms in the equation.
2. Add or subtract the same value to both sides of the equation.
3. Write the result as a single expression.

For example, if you have the equation $-m - 3 = 34$, you would simplify the equation as follows:

$-m - 3 + m = 34 + m$

$-3 = 34 + m$

Q: What is the final step in solving an equation involving a negative sign and parentheses?

A: The final step in solving an equation involving a negative sign and parentheses is to solve for the variable. This means that you will isolate the variable on one side of the equation.

Q: How do I solve for the variable?

A: To solve for the variable, you can use the following steps:

1. Add or subtract the same value to both sides of the equation.
2. Write the result as a single expression.
3. Identify the variable and its value.

For example, if you have the equation $-3 = 34 + m$, you would solve for the variable as follows:

$-3 - 34 = m$

$-37 = m$

Q: What are some common mistakes to avoid when solving equations involving negative signs and parentheses?

A: Some common mistakes to avoid when solving equations involving negative signs and parentheses include:

• Failing to distribute the negative sign to each term inside the parentheses.
• Not combining like terms when simplifying the equation.
• Adding or subtracting different values to both sides of the equation.

Q: How can I practice solving equations involving negative signs and parentheses?

A: You can practice solving equations involving negative signs and parentheses by:

• Working through examples and exercises in a textbook or online resource.
• Creating your own equations and solving them.
• Using online tools or software to generate random equations and solve them.

Q: What are some real-world applications of solving equations involving negative signs and parentheses?

A: Some real-world applications of solving equations involving negative signs and parentheses include:

• Physics: Solving equations to describe the motion of objects.
• Economics: Modeling the behavior of markets.
• Computer Science: Optimizing algorithms.

Q: How can I improve my skills in solving equations involving negative signs and parentheses?

A: You can improve your skills in solving equations involving negative signs and parentheses by:

• Practicing regularly.
• Seeking help from a teacher or tutor.
• Using online resources and tools to generate random equations and solve them.

Conclusion

Solving equations involving negative signs and parentheses may seem challenging at first, but with practice and patience, it becomes easier. Remember to distribute the negative sign, simplify the equation, add or subtract the same value to both sides, and finally solve for the variable. With these steps, you will be able to solve any equation involving negative signs and parentheses.