Solve For X X X : − 4 X − 1 = − 8 X − 1 -4x - 1 = -8x - 1 − 4 X − 1 = − 8 X − 1

Mar 11, 2025 by ADMIN 80 views

**Solving Linear Equations: A Step-by-Step Guide**

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 a specific linear equation, $-4x - 1 = -8x - 1$ , and provide a step-by-step guide on how to approach it.

What are Linear Equations?

A linear equation is an equation in which the highest power of the variable (in this case, $x$ ) is 1. Linear equations can be written in the form $ax + b = c$ , where $a$ , $b$ , and $c$ are constants, and $x$ is the variable.

The Equation to Solve

The equation we will be solving is $-4x - 1 = -8x - 1$ . This equation is a linear equation, and we will use the steps outlined below to solve for $x$ .

Step 1: Add or Subtract the Same Value to Both Sides

To solve for $x$ , we need to isolate the variable on one side of the equation. In this case, we can add $4x$ to both sides of the equation to get rid of the negative term.

-4x - 1 = -8x - 1
4x + 4x = 8x - 8x
8x - 1 = -1

Step 2: Add or Subtract the Same Value to Both Sides (Again)

Now that we have $8x - 1 = -1$ , we can add 1 to both sides of the equation to get rid of the negative term.

8x - 1 + 1 = -1 + 1
8x = 0

Step 3: Divide Both Sides by the Coefficient

Now that we have $8x = 0$ , we can divide both sides of the equation by 8 to solve for $x$ .

8x / 8 = 0 / 8
x = 0

Conclusion

In this article, we solved the linear equation $-4x - 1 = -8x - 1$ using a step-by-step approach. We added or subtracted the same value to both sides of the equation to isolate the variable, and then divided both sides by the coefficient to solve for $x$ . The final solution is $x = 0$ .

Tips and Tricks

When solving linear equations, it's essential to follow the order of operations (PEMDAS) to ensure that you are performing the correct operations.
When adding or subtracting the same value to both sides of the equation, make sure to do so on both sides of the equation.
When dividing both sides of the equation by a coefficient, make sure to do so on both sides of the equation.

Real-World Applications

Solving linear equations has numerous real-world applications, including:

Physics: Linear equations are used to describe the motion of objects under constant acceleration.
Engineering: Linear equations are used to design and optimize systems, such as electrical circuits and mechanical systems.
Economics: Linear equations are used to model economic systems and make predictions about future economic trends.

Common Mistakes to Avoid

When solving linear equations, it's essential to avoid common mistakes, including:

Not following the order of operations (PEMDAS): Failing to follow the order of operations can lead to incorrect solutions.
Not adding or subtracting the same value to both sides of the equation: Failing to add or subtract the same value to both sides of the equation can lead to incorrect solutions.
Not dividing both sides of the equation by the coefficient: Failing to divide both sides of the equation by the coefficient can lead to incorrect solutions.

Conclusion

Introduction

In our previous article, we discussed how to solve linear equations using a step-by-step approach. In this article, we will provide a Q&A guide to help you better understand the concept of solving linear equations.

Q: What is a linear equation?

A: A linear equation is an equation in which the highest power of the variable (in this case, $x$ ) is 1. Linear equations 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 or subtracting the same value to both sides of the equation, and then dividing both sides by the coefficient.

Q: What is the order of operations (PEMDAS)?

A: The order of operations (PEMDAS) is a set of rules that tells you which operations to perform first when solving an equation. The acronym PEMDAS stands for:

P: Parentheses (evaluate expressions inside parentheses first)
E: Exponents (evaluate any exponential expressions next)
M: Multiplication and Division (evaluate any multiplication and division operations from left to right)
A: Addition and Subtraction (evaluate any addition and subtraction operations from left to right)

Q: How do I add or subtract the same value to both sides of the equation?

A: To add or subtract the same value to both sides of the equation, you need to perform the same operation on both sides of the equation. For example, if you want to add 3 to both sides of the equation, you would add 3 to the left side of the equation and add 3 to the right side of the equation.

Q: How do I divide both sides of the equation by the coefficient?

A: To divide both sides of the equation by the coefficient, you need to perform the division operation on both sides of the equation. For example, if you want to divide both sides of the equation by 2, you would divide the left side of the equation by 2 and divide the right side of the equation by 2.

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

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

Not following the order of operations (PEMDAS): Failing to follow the order of operations can lead to incorrect solutions.
Not adding or subtracting the same value to both sides of the equation: Failing to add or subtract the same value to both sides of the equation can lead to incorrect solutions.
Not dividing both sides of the equation by the coefficient: Failing to divide both sides of the equation by the coefficient can lead to incorrect solutions.

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

A: To check your solution to a linear equation, you need to plug your solution back into the original equation and see if it is true. If your solution is correct, the equation should be true. If your solution is incorrect, the equation should not be true.

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

A: Solving linear equations has numerous real-world applications, including:

Physics: Linear equations are used to describe the motion of objects under constant acceleration.
Engineering: Linear equations are used to design and optimize systems, such as electrical circuits and mechanical systems.
Economics: Linear equations are used to model economic systems and make predictions about future economic trends.

Conclusion

In conclusion, solving linear equations is a crucial skill for students and professionals alike. By following the steps outlined in this article, you can solve linear equations with ease. Remember to follow the order of operations (PEMDAS), add or subtract the same value to both sides of the equation, and divide both sides of the equation by the coefficient to ensure that you are solving the equation correctly.