What Is The Value Of $m$ In The Equation $2m - (m + 1) = 0$?

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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 manipulate and simplify equations to find the value of unknown variables. In this article, we will focus on solving a specific linear equation, $2m - (m + 1) = 0$, and determine the value of $m$.

Understanding the Equation

The given equation is $2m - (m + 1) = 0$. To solve for $m$, we need to isolate the variable on one side of the equation. The equation involves a combination of addition, subtraction, multiplication, and division operations. Our goal is to simplify the equation and find the value of $m$ that satisfies the equation.

Distributive Property and Simplification

To simplify the equation, we can use the distributive property, which states that for any real numbers $a$, $b$, and $c$, $a(b + c) = ab + ac$. Applying this property to the given equation, we get:

2m−(m+1)=2m−m−12m - (m + 1) = 2m - m - 1

This simplifies to:

2m−m−1=m−12m - m - 1 = m - 1

Combining Like Terms

Now that we have simplified the equation, we can combine like terms. In this case, we have two terms with the variable $m$, which are $2m$ and $-m$. Combining these terms, we get:

m−1=m−1m - 1 = m - 1

This equation is now in a simpler form, but we still need to isolate the variable $m$.

Isolating the Variable

To isolate the variable $m$, we can add $1$ to both sides of the equation. This will cancel out the $-1$ on the right-hand side, leaving us with:

m=mm = m

However, this equation is not very helpful, as it does not provide any information about the value of $m$. To find the value of $m$, we need to go back to the original equation and try a different approach.

Using Algebraic Manipulation

Let's go back to the original equation and try a different approach. We can start by distributing the negative sign to the terms inside the parentheses:

2m−(m+1)=2m−m−12m - (m + 1) = 2m - m - 1

This simplifies to:

m−1=0m - 1 = 0

Now, we can add $1$ to both sides of the equation to isolate the variable $m$:

m=1m = 1

Conclusion

In this article, we have solved the linear equation $2m - (m + 1) = 0$ and determined the value of $m$. We used algebraic manipulation and simplification techniques to isolate the variable and find the solution. The final answer is $m = 1$.

Frequently Asked Questions

  • What is the value of $m$ in the equation $2m - (m + 1) = 0$?
  • How do you solve a linear equation with a combination of addition, subtraction, multiplication, and division operations?
  • What is the distributive property, and how is it used in algebraic manipulation?

Final Answer

The final answer is: 1\boxed{1}

Introduction

Solving linear equations is a fundamental concept in mathematics, and it is essential to understand how to manipulate and simplify equations to find the value of unknown variables. In this article, we will answer some frequently asked questions related to solving linear equations, including how to simplify equations, how to isolate variables, and how to use algebraic manipulation to solve equations.

Q&A: Solving Linear Equations

Q: What is the value of $m$ in the equation $2m - (m + 1) = 0$?

A: The value of $m$ in the equation $2m - (m + 1) = 0$ is $m = 1$. To solve for $m$, we used algebraic manipulation and simplification techniques to isolate the variable.

Q: How do you solve a linear equation with a combination of addition, subtraction, multiplication, and division operations?

A: To solve a linear equation with a combination of addition, subtraction, multiplication, and division operations, we need to use algebraic manipulation and simplification techniques to isolate the variable. This may involve distributing the negative sign to the terms inside the parentheses, combining like terms, and adding or subtracting the same value to both sides of the equation.

Q: What is the distributive property, and how is it used in algebraic manipulation?

A: The distributive property is a fundamental concept in algebra that states that for any real numbers $a$, $b$, and $c$, $a(b + c) = ab + ac$. This property is used in algebraic manipulation to simplify equations and isolate variables. For example, in the equation $2m - (m + 1) = 0$, we used the distributive property to simplify the equation and isolate the variable $m$.

Q: How do you isolate a variable in a linear equation?

A: To isolate a variable in a linear equation, we need to use algebraic manipulation and simplification techniques to get the variable by itself on one side of the equation. This may involve adding or subtracting the same value to both sides of the equation, multiplying or dividing both sides of the equation by the same value, or using the distributive property to simplify the equation.

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. For example, the equation $2m - (m + 1) = 0$ is a linear equation, while the equation $m^2 + 2m + 1 = 0$ is a quadratic equation.

Q: How do you solve a quadratic equation?

A: To solve a quadratic equation, we need to use algebraic manipulation and simplification techniques to isolate the variable. This may involve factoring the equation, using the quadratic formula, or completing the square.

Conclusion

In this article, we have answered some frequently asked questions related to solving linear equations, including how to simplify equations, how to isolate variables, and how to use algebraic manipulation to solve equations. We have also discussed the difference between linear and quadratic equations and how to solve quadratic equations.

Final Answer

The final answer is: 1\boxed{1}