Solve $\frac{2(n+17)}{8}=\frac{3}{8}$.Show Your Work!

Introduction

In this article, we will be solving a linear equation involving fractions. The equation is $\frac{2(n+17)}{8}=\frac{3}{8}$. We will break down the solution into manageable steps, making it easy to follow and understand.

Step 1: Multiply Both Sides by the Denominator

The first step in solving this equation is to eliminate the fractions. We can do this by multiplying both sides of the equation by the denominator, which is 8.

$\frac{2(n+17)}{8}=\frac{3}{8}$

Multiply both sides by 8:

$2(n+17) = 3$

Step 2: Distribute the 2

Next, we need to distribute the 2 to the terms inside the parentheses.

$2(n+17) = 3$

Distribute the 2:

$2n + 34 = 3$

Step 3: Subtract 34 from Both Sides

Now, we need to isolate the term with the variable. We can do this by subtracting 34 from both sides of the equation.

$2n + 34 = 3$

Subtract 34 from both sides:

$2n = -31$

Step 4: Divide Both Sides by 2

Finally, we need to solve for the variable by dividing both sides of the equation by 2.

$2n = -31$

Divide both sides by 2:

$n = -\frac{31}{2}$

Conclusion

In this article, we solved the linear equation $\frac{2(n+17)}{8}=\frac{3}{8}$ by following a series of steps. We multiplied both sides by the denominator, distributed the 2, subtracted 34 from both sides, and finally divided both sides by 2. The solution to the equation is $n = -\frac{31}{2}$.

Why is this Important?

Solving linear equations is an essential skill in mathematics, and it has many real-world applications. For example, in physics, linear equations are used to describe the motion of objects. In economics, linear equations are used to model the behavior of markets. In computer science, linear equations are used to solve systems of equations.

Tips and Tricks

Here are some tips and tricks to help you solve linear equations:

• Always start by eliminating the fractions by multiplying both sides by the denominator.
• Distribute the coefficients to the terms inside the parentheses.
• Isolate the term with the variable by adding or subtracting the same value from both sides.
• Finally, divide both sides by the coefficient to solve for the variable.

Common Mistakes

Here are some common mistakes to avoid when solving linear equations:

• Not eliminating the fractions by multiplying both sides by the denominator.
• Not distributing the coefficients to the terms inside the parentheses.
• Not isolating the term with the variable by adding or subtracting the same value from both sides.
• Not dividing both sides by the coefficient to solve for the variable.

Real-World Applications

Solving linear equations has many real-world applications. Here are a few examples:

• Physics: Linear equations are used to describe the motion of objects. For example, the equation $s = ut + \frac{1}{2}at^2$ describes the position of an object as a function of time.
• Economics: Linear equations are used to model the behavior of markets. For example, the equation $p = mc + b$ describes the price of a good as a function of its quantity.
• Computer Science: Linear equations are used to solve systems of equations. For example, the equation $Ax = b$ describes a system of linear equations, where $A$ is a matrix, $x$ is a vector of variables, and $b$ is a vector of constants.

Conclusion

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Introduction

In our previous article, we solved the linear equation $\frac{2(n+17)}{8}=\frac{3}{8}$ by following a series of steps. In this article, we will answer some frequently asked questions about solving linear equations.

Q: What is a linear 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.

Q: How do I solve a linear equation?

A: To solve a linear equation, you need to follow these steps:

1. Eliminate the fractions by multiplying both sides by the denominator.
2. Distribute the coefficients to the terms inside the parentheses.
3. Isolate the term with the variable by adding or subtracting the same value from both sides.
4. Finally, divide both sides by the coefficient to solve for the variable.

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 $x^2 + 4x + 4 = 0$ is a quadratic equation.

Q: How do I know if an equation is linear or quadratic?

A: To determine if an equation is linear or quadratic, you need to look at the highest power of the variable. If the highest power is 1, then the equation is linear. If the highest power is 2, then the equation is quadratic.

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

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

• Not eliminating the fractions by multiplying both sides by the denominator.
• Not distributing the coefficients to the terms inside the parentheses.
• Not isolating the term with the variable by adding or subtracting the same value from both sides.
• Not dividing both sides by the coefficient to solve for the variable.

Q: How do I check my work when solving a linear equation?

A: To check your work when solving a linear equation, you need to plug the solution back into the original equation and make sure it is true. For example, if you solve the equation $2x + 3 = 5$ and get $x = 1$, you need to plug $x = 1$ back into the original equation and make sure it is true.

Q: What are some real-world applications of linear equations?

A: Linear equations have many real-world applications, including:

• Physics: Linear equations are used to describe the motion of objects. For example, the equation $s = ut + \frac{1}{2}at^2$ describes the position of an object as a function of time.
• Economics: Linear equations are used to model the behavior of markets. For example, the equation $p = mc + b$ describes the price of a good as a function of its quantity.
• Computer Science: Linear equations are used to solve systems of equations. For example, the equation $Ax = b$ describes a system of linear equations, where $A$ is a matrix, $x$ is a vector of variables, and $b$ is a vector of constants.

Conclusion

In this article, we answered some frequently asked questions about solving linear equations. We discussed the definition of a linear equation, the steps to solve a linear equation, and some common mistakes to avoid. We also discussed some real-world applications of linear equations and how to check your work when solving a linear equation.