Solve For \[$ X \$\].$\[ \frac{1}{5} X = -8 \\]

Introduction

Linear equations are a fundamental concept in mathematics, and solving them is a crucial skill for students and professionals alike. In this article, we will focus on solving linear equations with one variable, specifically the equation $\frac{1}{5}x = -8$. We will break down the solution process into manageable steps, making it easy to understand and apply.

Understanding the Equation

Before we dive into the solution, let's take a closer look at the equation $\frac{1}{5}x = -8$. This equation is a linear equation with one variable, $x$. The coefficient of $x$ is $\frac{1}{5}$, and the constant term is $-8$. Our goal is to isolate the variable $x$ and find its value.

Step 1: Multiply Both Sides by 5

To get rid of the fraction, we can multiply both sides of the equation by 5. This will eliminate the coefficient $\frac{1}{5}$ and make it easier to work with.

$$\frac{1}{5}x = -8$$

$$\frac{1}{5}x \times 5 = -8 \times 5$$

$$x = -40$$

Step 2: Simplify the Equation

Now that we have multiplied both sides by 5, we can simplify the equation by combining like terms.

$$x = -40$$

Step 3: Check the Solution

To ensure that our solution is correct, we can plug it back into the original equation and check if it satisfies the equation.

$$\frac{1}{5}x = -8$$

$$\frac{1}{5}(-40) = -8$$

$$-8 = -8$$

Since the equation holds true, we can confirm that our solution is correct.

Conclusion

Solving linear equations with one variable is a straightforward process that requires attention to detail and a step-by-step approach. By following the steps outlined in this article, you can solve equations like $\frac{1}{5}x = -8$ with ease. Remember to multiply both sides by the reciprocal of the coefficient to eliminate the fraction, and then simplify the equation to find the value of the variable.

Real-World Applications

Linear equations have numerous real-world applications in fields such as physics, engineering, economics, and computer science. For example, in physics, linear equations can be used to model the motion of objects, while in economics, they can be used to analyze the relationship between variables such as supply and demand.

Tips and Tricks

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

• Always start by isolating the variable on one side of the equation.
• Use the reciprocal of the coefficient to eliminate fractions.
• Simplify the equation by combining like terms.
• Check your solution by plugging it back into the original equation.

Common Mistakes

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

• Failing to isolate the variable on one side of the equation.
• Not using the reciprocal of the coefficient to eliminate fractions.
• Not simplifying the equation by combining like terms.
• Not checking the solution by plugging it back into the original equation.

Conclusion

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Introduction

In our previous article, we discussed how to solve linear equations with one variable, specifically the equation $\frac{1}{5}x = -8$. We broke down the solution process into manageable steps and provided tips and tricks to help you solve linear equations with ease. In this article, we will answer some frequently asked questions about solving linear equations with one variable.

Q: What is a linear equation?

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

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

A: To determine if an equation is linear, look for the highest power of the variable. If the highest power is 1, then the equation is linear. For example, the equation $2x = 5$ is linear because the highest power of $x$ is 1.

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 $x^2 = 4$ is a quadratic equation because the highest power of $x$ is 2.

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

A: To solve a linear equation with a fraction, multiply both sides of the equation by the reciprocal of the coefficient of the variable. For example, to solve the equation $\frac{1}{5}x = -8$, multiply both sides by 5 to eliminate the fraction.

Q: What is the reciprocal of a fraction?

A: The reciprocal of a fraction is obtained by swapping the numerator and denominator. For example, the reciprocal of $\frac{1}{5}$ is $\frac{5}{1}$, which is equal to 5.

Q: How do I check my solution to a linear equation?

A: To check your solution to a linear equation, plug it back into the original equation and see if it satisfies the equation. For example, to check the solution $x = -40$ to the equation $\frac{1}{5}x = -8$, plug $x = -40$ back into the equation and see if it is true.

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

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

• Failing to isolate the variable on one side of the equation.
• Not using the reciprocal of the coefficient to eliminate fractions.
• Not simplifying the equation by combining like terms.
• Not checking the solution by plugging it back into the original equation.

Q: How can I practice solving linear equations?

A: There are many ways to practice solving linear equations, including:

• Working through practice problems in a textbook or online resource.
• Using online tools or apps to generate random linear equations.
• Creating your own linear equations and solving them.
• Joining a study group or working with a tutor to practice solving linear equations.

Conclusion

Solving linear equations with one variable is a fundamental skill that requires attention to detail and a step-by-step approach. By following the steps outlined in this article and practicing regularly, you can become proficient in solving linear equations and apply them to real-world problems. Remember to multiply both sides by the reciprocal of the coefficient to eliminate the fraction, and then simplify the equation to find the value of the variable. With practice and patience, you can become a master of solving linear equations.