What Is The Solution For The Equation?\[$-\frac{5}{2}=\frac{3}{4}+n\$\]A. \[$n=-\frac{13}{4}\$\]B. \[$n=-\frac{7}{4}\$\]C. \[$n=\frac{7}{4}\$\]D. \[$n=\frac{13}{4}\$\]

Introduction

In mathematics, solving equations is a fundamental concept that helps us understand the relationship between variables and constants. When we encounter an equation, our goal is to isolate the variable and find its value. In this article, we will focus on solving a specific equation, which is given as:

$$-\frac{5}{2}=\frac{3}{4}+n$$

Our objective is to find the value of the variable $n$.

Understanding the Equation

Before we dive into solving the equation, let's break it down and understand its components. The equation is a linear equation, which means it can be represented in the form of $ax + b = c$, where $a$, $b$, and $c$ are constants, and $x$ is the variable.

In this case, the equation is:

$$-\frac{5}{2}=\frac{3}{4}+n$$

We can see that the left-hand side of the equation is a constant, while the right-hand side is an expression involving the variable $n$.

Solving the Equation

To solve the equation, we need to isolate the variable $n$. We can do this by subtracting $\frac{3}{4}$ from both sides of the equation.

$$-\frac{5}{2} - \frac{3}{4} = n$$

Now, we need to find a common denominator for the fractions on the left-hand side. The least common multiple of $2$ and $4$ is $4$, so we can rewrite the fractions with a common denominator of $4$.

$$-\frac{5}{2} \cdot \frac{2}{2} - \frac{3}{4} = n$$

$$-\frac{10}{4} - \frac{3}{4} = n$$

Now, we can combine the fractions on the left-hand side.

$$-\frac{13}{4} = n$$

Therefore, the value of the variable $n$ is $-\frac{13}{4}$.

Conclusion

In this article, we solved a linear equation involving a variable $n$. We started by understanding the components of the equation and then isolated the variable $n$ by subtracting $\frac{3}{4}$ from both sides of the equation. We found that the value of $n$ is $-\frac{13}{4}$.

Final Answer

The final answer to the equation is:

$$n = -\frac{13}{4}$$

This is option A in the given multiple-choice question.

Comparison with Other Options

Let's compare our solution with the other options:

• Option B: $n = -\frac{7}{4}$
• Option C: $n = \frac{7}{4}$
• Option D: $n = \frac{13}{4}$

Our solution, $n = -\frac{13}{4}$, is different from all the other options. This confirms that our solution is correct.

Importance of Solving Equations

Solving equations is an essential skill in mathematics and has numerous applications in real-life situations. It helps us understand the relationship between variables and constants, which is crucial in fields like physics, engineering, and economics.

In conclusion, solving equations is a fundamental concept in mathematics that requires a deep understanding of algebraic manipulations. By following the steps outlined in this article, we can solve linear equations involving variables and constants.

Frequently Asked Questions

• Q: What is the solution to the equation $-\frac{5}{2}=\frac{3}{4}+n$? A: The solution to the equation is $n = -\frac{13}{4}$.
• Q: How do I solve a linear equation involving a variable? A: To solve a linear equation, you need to isolate the variable by performing algebraic manipulations, such as adding or subtracting fractions.
• Q: What is the importance of solving equations? A: Solving equations is essential in mathematics and has numerous applications in real-life situations, such as physics, engineering, and economics.

References

• [1] Algebra, 2nd edition, by Michael Artin
• [2] Linear Algebra and Its Applications, 4th edition, by Gilbert Strang
• [3] Mathematics for Engineers and Scientists, 6th edition, by James Stewart
  

Introduction

Solving equations is a fundamental concept in mathematics that requires a deep understanding of algebraic manipulations. In our previous article, we solved a linear equation involving a variable $n$. In this article, we will address some frequently asked questions (FAQs) on solving equations.

Q&A

Q: What is the solution to the equation $-\frac{5}{2}=\frac{3}{4}+n$?

A: The solution to the equation is $n = -\frac{13}{4}$.

Q: How do I solve a linear equation involving a variable?

A: To solve a linear equation, you need to isolate the variable by performing algebraic manipulations, such as adding or subtracting fractions. You can also use inverse operations, such as multiplying or dividing both sides of the equation by a constant, to isolate the variable.

Q: What is the importance of solving equations?

A: Solving equations is essential in mathematics and has numerous applications in real-life situations, such as physics, engineering, and economics. It helps us understand the relationship between variables and constants, which is crucial in making predictions and decisions.

Q: How do I simplify a fraction?

A: To simplify a fraction, you need to find the greatest common divisor (GCD) of the numerator and denominator. You can then divide both the numerator and denominator by the GCD to simplify the fraction.

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, $2x + 3 = 5$ is a linear equation, while $x^2 + 4x + 4 = 0$ is a quadratic equation.

Q: How do I solve a quadratic equation?

A: To solve a quadratic equation, you can use the quadratic formula, which is given by:

$$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$

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

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

A: The order of operations is crucial in solving equations. It ensures that we perform the operations in the correct order, which is:

1. Parentheses
2. Exponents
3. Multiplication and Division
4. Addition and Subtraction

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

A: To check your solution to an equation, you need to substitute the value of the variable into the original equation and verify that it is true. If the equation is true, then your solution is correct.

Conclusion

Solving equations is a fundamental concept in mathematics that requires a deep understanding of algebraic manipulations. By following the steps outlined in this article, you can solve linear and quadratic equations involving variables and constants. Remember to simplify fractions, use inverse operations, and check your solution to ensure that it is correct.

Frequently Asked Questions (FAQs) on Solving Equations

• Q: What is the solution to the equation $-\frac{5}{2}=\frac{3}{4}+n$? A: The solution to the equation is $n = -\frac{13}{4}$.
• Q: How do I solve a linear equation involving a variable? A: To solve a linear equation, you need to isolate the variable by performing algebraic manipulations, such as adding or subtracting fractions.
• Q: What is the importance of solving equations? A: Solving equations is essential in mathematics and has numerous applications in real-life situations, such as physics, engineering, and economics.

References

• [1] Algebra, 2nd edition, by Michael Artin
• [2] Linear Algebra and Its Applications, 4th edition, by Gilbert Strang
• [3] Mathematics for Engineers and Scientists, 6th edition, by James Stewart