Solve: { -5x + 1 = 21$}$

Mar 12, 2025 by ADMIN 25 views

$Solve: ${$-5x + 1 = 21\$}$$

Introduction to Solving Linear Equations

Solving linear equations is a fundamental concept in mathematics, and it is essential to understand how to solve them to progress in various mathematical disciplines. A linear equation is an equation in which the highest power of the variable(s) is 1. In this article, we will focus on solving a linear equation of the form ${-5x + 1 = 21}$ . This equation involves a single variable, ${x}$ , and a constant term. Our goal is to isolate the variable ${x}$ and find its value.

Understanding the Equation

The given equation is ${-5x + 1 = 21}$ . To solve for ${x}$ , we need to isolate the variable on one side of the equation. The equation involves a negative coefficient, which means that the variable ${x}$ is being multiplied by a negative number. This will affect the direction of the solution.

Step 1: Subtract 1 from Both Sides

To begin solving the equation, we need to get rid of the constant term on the left side of the equation. We can do this by subtracting 1 from both sides of the equation. This will keep the equation balanced and allow us to isolate the variable.

${-5x + 1 - 1 = 21 - 1}$

Simplifying the equation, we get:

${-5x = 20}$

Step 2: Divide Both Sides by -5

Now that we have isolated the variable term, we need to get rid of the coefficient. In this case, the coefficient is -5, which means that we need to divide both sides of the equation by -5. This will give us the value of the variable ${x}$ .

${\frac{-5x}{-5} = \frac{20}{-5}}$

Simplifying the equation, we get:

${x = -4}$

Conclusion

In this article, we solved a linear equation of the form ${-5x + 1 = 21}$ . We used the steps of subtracting 1 from both sides and then dividing both sides by -5 to isolate the variable ${x}$ . The final solution is ${x = -4}$ . This demonstrates the importance of following the correct steps when solving linear equations.

Tips and Tricks for Solving Linear Equations

When solving linear equations, it is essential to follow the correct steps to ensure that the equation is balanced and that the variable is isolated. Here are some tips and tricks to help you solve linear equations:

Check your work: Always check your work by plugging the solution back into the original equation to ensure that it is true.
Use inverse operations: Use inverse operations to get rid of the coefficient and isolate the variable.
Simplify the equation: Simplify the equation as you go to make it easier to solve.
Check for extraneous solutions: Check for extraneous solutions by plugging the solution back into the original equation.

Common Mistakes to Avoid

When solving linear equations, there are several common mistakes to avoid. Here are some of the most common mistakes:

Not checking your work: Failing to check your work can lead to incorrect solutions.
Not using inverse operations: Failing to use inverse operations can make it difficult to isolate the variable.
Not simplifying the equation: Failing to simplify the equation can make it difficult to solve.
Not checking for extraneous solutions: Failing to check for extraneous solutions can lead to incorrect solutions.

Real-World Applications of Solving Linear Equations

Solving linear equations has numerous real-world applications. Here are some examples:

Finance: Solving linear equations is used in finance to calculate interest rates, investment returns, and other financial metrics.
Science: Solving linear equations is used in science to model population growth, chemical reactions, and other scientific phenomena.
Engineering: Solving linear equations is used in engineering to design and optimize systems, such as bridges, buildings, and electronic circuits.
Computer Science: Solving linear equations is used in computer science to solve problems in machine learning, data analysis, and other areas.

Conclusion

Solving linear equations is a fundamental concept in mathematics, and it has numerous real-world applications. By following the correct steps and avoiding common mistakes, you can solve linear equations with ease. Whether you are a student, a professional, or simply someone who wants to learn, solving linear equations is an essential skill to have.

Introduction

Solving linear equations is a fundamental concept in mathematics, and it is essential to understand how to solve them to progress in various mathematical disciplines. In this article, we will provide a Q&A section to help you better understand how to solve linear equations.

Q: What is a linear equation?

A: A linear equation is an equation in which the highest power of the variable(s) is 1. It is a simple equation that can be solved using basic algebraic operations.

Q: What are the steps to solve a linear equation?

A: The steps to solve a linear equation are:

Check if the equation is linear: Make sure that the equation is in the form of ax + b = c, where a, b, and c are constants.
Add or subtract the same value to both sides: Add or subtract the same value to both sides of the equation to get rid of the constant term.
Multiply or divide both sides by the same value: Multiply or divide both sides of the equation by the same value to get rid of the coefficient.
Check your work: Plug the solution back into the original equation to ensure that it is true.

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

Q: How do I solve a linear equation with a negative coefficient?

A: To solve a linear equation with a negative coefficient, you need to follow the same steps as solving a linear equation with a positive coefficient. However, you need to be careful when multiplying or dividing both sides of the equation by a negative value, as it will change the direction of the solution.

Q: What is the importance of checking your work when solving linear equations?

A: Checking your work is essential when solving linear equations to ensure that the solution is correct. If you do not check your work, you may end up with an incorrect solution, which can lead to errors in further calculations.

Q: Can I use a calculator to solve linear equations?

A: Yes, you can use a calculator to solve linear equations. However, it is essential to understand the steps involved in solving linear equations, as using a calculator without understanding the underlying math can lead to errors.

Q: How do I solve a linear equation with multiple variables?

A: To solve a linear equation with multiple variables, you need to follow the same steps as solving a linear equation with a single variable. However, you need to be careful when multiplying or dividing both sides of the equation by a value that involves multiple variables.

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

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

Not checking your work: Failing to check your work can lead to incorrect solutions.
Not using inverse operations: Failing to use inverse operations can make it difficult to isolate the variable.
Not simplifying the equation: Failing to simplify the equation can make it difficult to solve.
Not checking for extraneous solutions: Failing to check for extraneous solutions can lead to incorrect solutions.