Solve For { M $} . . . { 2(m + 3) = 18 \}

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Introduction to Solving Linear Equations

Solving linear equations is a fundamental concept in mathematics, and it is essential to understand how to isolate variables in order to find their values. In this article, we will focus on solving a linear equation with a single variable, $m$. The given equation is $2(m + 3) = 18$. Our goal is to isolate $m$ and find its value.

Understanding the Equation

The given equation is a linear equation with a single variable, $m$. The equation is in the form of $2(m + 3) = 18$, where $2$ is the coefficient of the variable, and $m + 3$ is the expression inside the parentheses. To solve for $m$, we need to isolate the variable by getting rid of the coefficient and the expression inside the parentheses.

Distributive Property

To solve for $m$, we can use the distributive property, which states that for any real numbers $a$, $b$, and $c$, $a(b + c) = ab + ac$. We can apply this property to the given equation by distributing the coefficient $2$ to the expression inside the parentheses.

Distributing the Coefficient

Using the distributive property, we can rewrite the equation as:

$$2(m + 3) = 2m + 6$$

This is because $2(m + 3)$ is equal to $2m + 6$, where $2m$ is the result of multiplying $2$ by $m$, and $6$ is the result of multiplying $2$ by $3$.

Simplifying the Equation

Now that we have distributed the coefficient, we can simplify the equation by combining like terms. The equation is now:

$$2m + 6 = 18$$

We can simplify this equation by subtracting $6$ from both sides, which gives us:

$$2m = 12$$

Isolating the Variable

Now that we have isolated the variable by getting rid of the constant term, we can solve for $m$ by dividing both sides of the equation by $2$. This gives us:

$$m = 6$$

Therefore, the value of $m$ is $6$.

Conclusion

In this article, we solved a linear equation with a single variable, $m$. We used the distributive property to distribute the coefficient to the expression inside the parentheses, and then simplified the equation by combining like terms. Finally, we isolated the variable by getting rid of the constant term and solved for $m$. The value of $m$ is $6$.

Frequently Asked Questions

• What is the distributive property? The distributive property is a mathematical concept that states that for any real numbers $a$, $b$, and $c$, $a(b + c) = ab + ac$.
• How do I solve a linear equation with a single variable? To solve a linear equation with a single variable, you need to isolate the variable by getting rid of the coefficient and the expression inside the parentheses.
• What is the value of $m$ in the given equation? The value of $m$ in the given equation is $6$.

Additional Resources

• Linear Equations
• Distributive Property
• Mathematics

Step-by-Step Solution

1. Distribute the coefficient to the expression inside the parentheses using the distributive property.
2. Simplify the equation by combining like terms.
3. Isolate the variable by getting rid of the constant term.
4. Solve for $m$ by dividing both sides of the equation by the coefficient.

Example Problems

• Solve for $x$ in the equation $3(x + 2) = 15$.
• Solve for $y$ in the equation $2(y - 3) = 10$.

Real-World Applications

• Solving linear equations is used in a variety of real-world applications, such as finance, engineering, and physics.
• Linear equations are used to model real-world situations, such as the motion of objects, the flow of fluids, and the growth of populations.

Conclusion

In conclusion, solving linear equations is a fundamental concept in mathematics that is used to isolate variables and find their values. In this article, we solved a linear equation with a single variable, $m$, using the distributive property and simplifying the equation by combining like terms. The value of $m$ is $6$. We also provided additional resources, step-by-step solutions, example problems, and real-world applications to help readers understand the concept of solving linear equations.

Introduction

Solving linear equations is a fundamental concept in mathematics that is used to isolate variables and find their values. In our previous article, we solved a linear equation with a single variable, $m$, using the distributive property and simplifying the equation by combining like terms. In this article, we will provide a Q&A section to help readers understand the concept of solving linear equations and provide additional resources and examples.

Q&A

Q: What is the distributive property?

A: The distributive property is a mathematical concept that states that for any real numbers $a$, $b$, and $c$, $a(b + c) = ab + ac$. This property is used to distribute a coefficient to an expression inside parentheses.

Q: How do I solve a linear equation with a single variable?

A: To solve a linear equation with a single variable, you need to isolate the variable by getting rid of the coefficient and the expression inside the parentheses. This can be done by using the distributive property, simplifying the equation by combining like terms, and isolating the variable.

Q: What is the value of $m$ in the given equation?

A: The value of $m$ in the given equation is $6$. This was found by isolating the variable and solving for $m$.

Q: Can I use the distributive property to solve a linear equation with a single variable?

A: Yes, the distributive property can be used to solve a linear equation with a single variable. This property is used to distribute a coefficient to an expression inside parentheses, which can help to simplify the equation and isolate the variable.

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

A: To simplify a linear equation by combining like terms, you need to identify the like terms in the equation and combine them. Like terms are terms that have the same variable and coefficient. For example, in the equation $2x + 3x = 5x$, the like terms are $2x$ and $3x$, which can be combined to get $5x$.

Q: Can I use a calculator to solve a linear equation?

A: Yes, a calculator can be used to solve a linear equation. However, it is also important to understand the concept of solving linear equations and to be able to solve them by hand. This will help you to understand the underlying mathematics and to be able to solve more complex equations.

Q: How do I know if an equation is linear or not?

A: An equation is linear if it can be written in the form $ax + b = c$, where $a$, $b$, and $c$ are constants and $x$ is the variable. If an equation cannot be written in this form, it is not linear.

Additional Resources

• Linear Equations
• Distributive Property
• Mathematics

Step-by-Step Solutions

• Solve for $x$ in the equation $3(x + 2) = 15$.
• Solve for $y$ in the equation $2(y - 3) = 10$.

Example Problems

• Solve for $z$ in the equation $4(z + 1) = 20$.
• Solve for $w$ in the equation $3(w - 2) = 15$.

Real-World Applications

• Solving linear equations is used in a variety of real-world applications, such as finance, engineering, and physics.
• Linear equations are used to model real-world situations, such as the motion of objects, the flow of fluids, and the growth of populations.

Conclusion

In conclusion, solving linear equations is a fundamental concept in mathematics that is used to isolate variables and find their values. In this article, we provided a Q&A section to help readers understand the concept of solving linear equations and provide additional resources and examples. We also provided step-by-step solutions and example problems to help readers practice solving linear equations.