What Is The Value Of $n$ In The Equation $\frac{1}{2}(n-4)-3=3-(2n+3)$?A. $ N = 0 N=0 N = 0 [/tex] B. $n=2$ C. $n=4$ D. $ N = 6 N=6 N = 6 [/tex]

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Introduction

In this article, we will delve into the world of algebra and solve for the value of $n$ in the given equation $\frac{1}{2}(n-4)-3=3-(2n+3)$. This equation involves basic algebraic operations such as addition, subtraction, multiplication, and division, as well as the use of parentheses to group terms. Our goal is to isolate the variable $n$ and determine its value.

Step 1: Simplify the Equation

To begin solving the equation, we need to simplify it by combining like terms and eliminating any parentheses. We can start by distributing the $\frac{1}{2}$ to the terms inside the parentheses on the left-hand side of the equation.

12(n−4)−3=3−(2n+3)\frac{1}{2}(n-4)-3=3-(2n+3)

12n−2−3=3−2n−3\frac{1}{2}n - 2 - 3 = 3 - 2n - 3

Now, let's simplify the right-hand side of the equation by combining the constants.

12n−5=−2n\frac{1}{2}n - 5 = -2n

Step 2: Isolate the Variable n

Next, we need to isolate the variable $n$ by getting all the terms containing $n$ on one side of the equation. We can start by adding $2n$ to both sides of the equation to eliminate the negative term.

12n−5+2n=−2n+2n\frac{1}{2}n - 5 + 2n = -2n + 2n

52n−5=0\frac{5}{2}n - 5 = 0

Now, let's add $5$ to both sides of the equation to eliminate the constant term.

52n=5\frac{5}{2}n = 5

Step 3: Solve for n

Finally, we can solve for $n$ by dividing both sides of the equation by $\frac{5}{2}$.

n=552n = \frac{5}{\frac{5}{2}}

n=2n = 2

Conclusion

In this article, we solved for the value of $n$ in the given equation $\frac{1}{2}(n-4)-3=3-(2n+3)$. By simplifying the equation, isolating the variable $n$, and solving for $n$, we determined that the value of $n$ is $2$. This solution demonstrates the importance of following the order of operations and using algebraic techniques to solve equations.

Answer

The correct answer is:

  • B. $n=2$

Additional Tips and Tricks

When solving equations, it's essential to follow the order of operations (PEMDAS) and use algebraic techniques to isolate the variable. Additionally, be sure to check your work by plugging the solution back into the original equation to ensure that it's true.

Common Mistakes to Avoid

When solving equations, some common mistakes to avoid include:

  • Not following the order of operations (PEMDAS)
  • Not using algebraic techniques to isolate the variable
  • Not checking the solution by plugging it back into the original equation

Q: What is the first step in solving an equation?

A: The first step in solving an equation is to simplify it by combining like terms and eliminating any parentheses. This helps to make the equation easier to work with and reduces the number of steps needed to solve it.

Q: How do I isolate the variable in an equation?

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

Q: What is the order of operations (PEMDAS)?

A: The order of operations (PEMDAS) is a set of rules that tells you which operations to perform first when working with mathematical expressions. The acronym PEMDAS stands for:

  • Parentheses: Evaluate expressions inside parentheses first.
  • Exponents: Evaluate any exponential expressions next.
  • Multiplication and Division: Evaluate any multiplication and division operations from left to right.
  • Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: How do I check my solution to an equation?

A: To check your solution to an equation, you need to plug the solution back into the original equation and see if it's true. If the solution satisfies the equation, then it's the correct solution.

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

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

  • Not following the order of operations (PEMDAS)
  • Not using algebraic techniques to isolate the variable
  • Not checking the solution by plugging it back into the original equation
  • Not simplifying the equation before solving it
  • Not being careful with negative signs and fractions

Q: How do I simplify an equation?

A: To simplify an equation, you need to combine like terms and eliminate any parentheses. This can be done by adding or subtracting the same value to both sides of the equation, or by 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. For example, the equation 2x + 3 = 5 is a linear equation. A quadratic equation, on the other hand, is an equation in which the highest power of the variable is 2. For example, the equation x^2 + 4x + 4 = 0 is a quadratic equation.

Q: How do I solve a quadratic equation?

A: To solve a quadratic equation, you need to use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

where a, b, and c are the coefficients of the quadratic equation.

Conclusion

In this article, we answered some frequently asked questions about solving equations. We covered topics such as simplifying equations, isolating variables, and checking solutions. We also discussed common mistakes to avoid and provided tips for solving linear and quadratic equations. By following these tips and avoiding common mistakes, you can become more confident and proficient in solving equations and algebraic problems.