Solve For N N N . − 5 6 N = 40 -\frac{5}{6} N = 40 − 6 5 ​ N = 40 A. N = − 56 N = -56 N = − 56 B. N = − 48 N = -48 N = − 48 C. N = 48 N = 48 N = 48 D. N = 56 N = 56 N = 56

Introduction

Linear equations are a fundamental concept in mathematics, and solving them is a crucial skill for students to master. In this article, we will focus on solving a specific type of linear equation, which involves isolating the variable $n$ on one side of the equation. We will use a step-by-step approach to solve the equation $-\frac{5}{6} n = 40$ and provide a detailed explanation of each step.

Understanding the Equation

The given equation is $-\frac{5}{6} n = 40$. This equation involves a fraction and a variable $n$. To solve for $n$, we need to isolate the variable on one side of the equation.

Step 1: Multiply Both Sides by the Reciprocal of the Coefficient

The first step in solving the equation is to multiply both sides by the reciprocal of the coefficient of $n$. In this case, the coefficient of $n$ is $-\frac{5}{6}$, and its reciprocal is $-\frac{6}{5}$.

-\frac{5}{6} n = 40
\Rightarrow -\frac{6}{5} \cdot \left(-\frac{5}{6} n\right) = -\frac{6}{5} \cdot 40

Step 2: Simplify the Equation

After multiplying both sides by the reciprocal of the coefficient, we can simplify the equation.

-\frac{6}{5} \cdot \left(-\frac{5}{6} n\right) = -\frac{6}{5} \cdot 40
\Rightarrow n = -\frac{6}{5} \cdot 40

Step 3: Evaluate the Expression

Now that we have simplified the equation, we can evaluate the expression on the right-hand side.

n = -\frac{6}{5} \cdot 40
\Rightarrow n = -\frac{240}{5}
\Rightarrow n = -48

Conclusion

In this article, we solved the linear equation $-\frac{5}{6} n = 40$ using a step-by-step approach. We multiplied both sides by the reciprocal of the coefficient, simplified the equation, and evaluated the expression to find the value of $n$. The final answer is $n = -48$.

Answer Key

A. $n = -56$ B. $n = -48$ C. $n = 48$ D. $n = 56$

The correct answer is B. $n = -48$.

Tips and Tricks

• When solving linear equations, it's essential to isolate the variable on one side of the equation.
• To isolate the variable, you can multiply both sides by the reciprocal of the coefficient.
• Simplify the equation after multiplying both sides by the reciprocal of the coefficient.
• Evaluate the expression on the right-hand side to find the value of the variable.

Practice Problems

1. Solve the equation $-\frac{3}{4} n = 30$.
2. Solve the equation $\frac{2}{3} n = 24$.
3. Solve the equation $-\frac{1}{2} n = 15$.

Solutions

1. $n = -40$
2. $n = 36$
3. $n = -30$

Conclusion

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Introduction

In our previous article, we solved the linear equation $-\frac{5}{6} n = 40$ using a step-by-step approach. We provided a detailed explanation of each step and offered tips and tricks for solving linear equations. In this article, we will continue to explore the concept of solving linear equations by answering some frequently asked questions.

Q&A

Q: What is a linear equation?

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

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. You can do this 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(s) is 1, while a quadratic equation is an equation in which the highest power of the variable(s) is 2. For example, $x + 2 = 3$ is a linear equation, while $x^2 + 2x + 1 = 0$ is a quadratic equation.

Q: How do I solve a linear equation with fractions?

A: To solve a linear equation with fractions, you need to multiply both sides of the equation by the reciprocal of the coefficient of the variable. This will eliminate the fraction and allow you to solve for the variable.

Q: What is the reciprocal of a fraction?

A: The reciprocal of a fraction is obtained by swapping the numerator and the denominator. For example, the reciprocal of $\frac{2}{3}$ is $\frac{3}{2}$.

Q: How do I simplify an expression?

A: To simplify an expression, you need to combine like terms and eliminate any unnecessary parentheses or brackets.

Q: What is a like term?

A: A like term is a term that has the same variable(s) raised to the same power. For example, $2x$ and $3x$ are like terms, while $2x$ and $3y$ are not like terms.

Q: How do I evaluate an expression?

A: To evaluate an expression, you need to substitute the values of the variables into the expression and simplify.

Q: What is the order of operations?

A: The order of operations is a set of rules that tells you which operations to perform first when evaluating an expression. The order of operations is:

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

Practice Problems

1. Solve the equation $2x + 3 = 5$.
2. Solve the equation $x - 2 = 3$.
3. Solve the equation $\frac{1}{2}x = 4$.

Solutions

1. $x = 1$
2. $x = 5$
3. $x = 8$

Conclusion

Solving linear equations is a crucial skill for students to master. In this article, we answered some frequently asked questions about solving linear equations and provided practice problems and solutions for readers to practice and reinforce their understanding of the concept. We hope this article has been helpful in clarifying any doubts you may have had about solving linear equations.