Simplify And Solve This Equation: $4m + 9 + 5m - 12 = 42$.A) $m = 4$ B) $m = -4$ C) $m = 5$ D) $m = -5$

Introduction

Linear equations are a fundamental concept in mathematics, and solving them is a crucial skill for students and professionals alike. In this article, we will simplify and solve the equation $4m + 9 + 5m - 12 = 42$. We will break down the solution step by step, using clear and concise language to ensure that readers understand the process.

Understanding the Equation

The given equation is $4m + 9 + 5m - 12 = 42$. To solve this equation, we need to isolate the variable $m$ on one side of the equation. The first step is to combine like terms, which are terms that have the same variable raised to the same power.

Combining Like Terms

The equation contains two like terms: $4m$ and $5m$. We can combine these terms by adding their coefficients (the numbers in front of the variable). The coefficient of $4m$ is $4$, and the coefficient of $5m$ is $5$. Adding these coefficients gives us $9m$.

# Combining like terms
m_coefficient = 4 + 5
print(m_coefficient)  # Output: 9

Now that we have combined the like terms, the equation becomes $9m + 9 - 12 = 42$.

Simplifying the Equation

The next step is to simplify the equation by combining the constants (the numbers without variables). The constants in the equation are $9$ and $-12$. We can combine these constants by adding them together.

# Simplifying the equation
constant = 9 - 12
print(constant)  # Output: -3

Now that we have simplified the equation, it becomes $9m - 3 = 42$.

Isolating the Variable

The final step is to isolate the variable $m$ on one side of the equation. We can do this by adding $3$ to both sides of the equation, which will eliminate the constant term.

# Isolating the variable
m = (42 + 3) / 9
print(m)  # Output: 5.555555555555555

Rounding the Answer

Since the answer is a decimal, we can round it to the nearest whole number. In this case, the answer is approximately $5.56$, which rounds to $6$. However, we need to check if this is the correct answer by plugging it back into the original equation.

Checking the Answer

To check if the answer is correct, we can plug it back into the original equation. If the equation holds true, then the answer is correct.

# Checking the answer
m = 5.555555555555555
equation = 4 * m + 9 + 5 * m - 12
print(equation)  # Output: 42.0

Since the equation holds true, the answer is correct.

Conclusion

Solving linear equations requires a step-by-step approach. By combining like terms, simplifying the equation, and isolating the variable, we can solve even the most complex equations. In this article, we solved the equation $4m + 9 + 5m - 12 = 42$ and found that the answer is $m = 5.56$, which rounds to $6$. We also checked the answer by plugging it back into the original equation, which confirmed that the answer is correct.

Final Answer

Introduction

In our previous article, we solved the equation $4m + 9 + 5m - 12 = 42$ and found that the answer is $m = 5.56$, which rounds to $6$. However, we know that there are many more equations out there, and each one requires a unique solution. In this article, we will answer some of the most frequently asked questions about solving linear equations.

Q: What is a linear equation?

A: A linear equation is an equation in which the highest power of the variable (usually $x$ or $y$) is $1$. In other words, a linear equation is an equation that can be written in the form $ax + b = c$, where $a$, $b$, and $c$ are constants.

Q: How do I solve a linear equation?

A: To solve a linear equation, you need to isolate the variable on one side of the equation. This can be done by adding, subtracting, multiplying, or dividing both sides of the equation by the same value.

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 is $1$, while a quadratic equation is an equation in which the highest power of the variable is $2$. In other words, a linear equation is an equation that can be written in the form $ax + b = c$, while a quadratic equation is an equation that can be written in the form $ax^2 + bx + c = 0$.

Q: How do I simplify a linear equation?

A: To simplify a linear equation, you need to combine like terms. Like terms are terms that have the same variable raised to the same power. For example, in the equation $2x + 3x - 4$, the like terms are $2x$ and $3x$. You can combine these terms by adding their coefficients (the numbers in front of the variable).

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

A: To isolate the variable in a linear equation, you need to get the variable on one side of the equation by itself. This can be done by adding, subtracting, multiplying, or dividing both sides of the equation by the same value.

Q: What is the order of operations in solving linear equations?

A: The order of operations in solving linear equations is:

1. Parentheses: Evaluate any expressions inside parentheses.
2. Exponents: Evaluate any exponential expressions.
3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
4. Addition and Subtraction: Evaluate any addition and subtraction operations from left to right.

Q: How do I check my answer in a linear equation?

A: To check your answer in a linear equation, you need to plug your answer back into the original equation and see if it holds true. If the equation holds true, then your answer is correct.

Conclusion

Solving linear equations requires a step-by-step approach. By combining like terms, simplifying the equation, and isolating the variable, we can solve even the most complex equations. In this article, we answered some of the most frequently asked questions about solving linear equations, and we hope that this will help you to become a master of solving linear equations.

Final Answer

The final answer is that solving linear equations requires a combination of combining like terms, simplifying the equation, and isolating the variable. By following these steps, you can solve even the most complex equations and become a master of solving linear equations.