Solving The Equation 13 - X = 21 A Step-by-Step Guide
In this article, we will delve into the process of solving for the unknown variable x in the linear equation 13 - x = 21. This type of equation is fundamental in algebra and is a crucial skill for various mathematical applications. We will break down the steps involved in isolating x and arriving at the solution. This detailed explanation aims to provide a comprehensive understanding for students and anyone interested in brushing up on their algebra skills. Understanding how to solve for variables is a cornerstone of mathematical proficiency, and mastering this skill will open doors to more advanced concepts and problem-solving techniques. Let's embark on this mathematical journey and unravel the value of x together. We will explore the step-by-step method, ensuring clarity and accuracy in our calculations. This exercise not only reinforces algebraic principles but also enhances logical reasoning and analytical skills. By the end of this article, you will be equipped with the knowledge and confidence to tackle similar equations effectively. Our focus will be on providing a clear, concise, and accessible explanation, making the learning process enjoyable and rewarding. So, let's dive in and discover the solution to this intriguing equation. We'll be using algebraic manipulation, a core concept in mathematics, to isolate x and determine its value. This process involves strategically performing operations on both sides of the equation to maintain balance and ultimately reveal the solution. Get ready to enhance your problem-solving skills and boost your understanding of algebra!
Understanding the Equation
The given equation is 13 - x = 21. Our primary goal is to isolate x on one side of the equation to determine its value. This involves using inverse operations to undo the operations performed on x. In this case, x is being subtracted from 13, and the result is 21. To isolate x, we need to eliminate the 13 from the left side of the equation. This requires a careful and systematic approach to ensure we maintain the equality of both sides. Understanding the equation is the first step towards finding the solution. We need to recognize the relationship between the numbers and the variable. This understanding will guide us in choosing the correct operations to perform. The equation represents a balance, where both sides are equal. Any operation performed on one side must also be performed on the other to maintain this balance. This principle is crucial in solving algebraic equations. We will use this principle throughout the process of solving for x. Our aim is to manipulate the equation in a way that x stands alone on one side, revealing its value. This process involves careful attention to detail and a thorough understanding of algebraic principles. By breaking down the equation and understanding its components, we can approach the problem with confidence and accuracy. This foundational understanding is essential for tackling more complex equations in the future.
Step-by-Step Solution
To isolate x, we need to subtract 13 from both sides of the equation. This is because subtracting 13 from the left side will cancel out the positive 13, leaving us with just -x. Performing this operation on both sides ensures that the equation remains balanced. So, we have:
13 - x - 13 = 21 - 13
This simplifies to:
-x = 8
Now, we have -x equal to 8. However, we want to find the value of x, not -x. To do this, we can multiply both sides of the equation by -1. This will change the sign of both sides, giving us the value of x. Multiplying both sides by -1, we get:
(-1) * (-x) = (-1) * 8
This simplifies to:
x = -8
Therefore, the value of x that satisfies the equation 13 - x = 21 is -8. This step-by-step solution demonstrates the systematic approach required to solve algebraic equations. Each step is carefully chosen to move closer to isolating the variable. The key is to perform the same operation on both sides of the equation to maintain balance. This ensures that the equality remains true throughout the process. By understanding each step and the reasoning behind it, you can apply these techniques to solve a variety of algebraic problems. This methodical approach builds confidence and accuracy in your problem-solving abilities. Remember, the goal is to isolate the variable, and each step should contribute towards achieving this goal. With practice, you'll become more proficient in recognizing the necessary operations and applying them effectively.
Verification
To ensure our solution is correct, we can substitute the value of x back into the original equation. If the equation holds true, then our solution is verified. Substituting x = -8 into the equation 13 - x = 21, we get:
13 - (-8) = 21
Remember that subtracting a negative number is the same as adding its positive counterpart. So, we have:
13 + 8 = 21
This simplifies to:
21 = 21
Since the equation holds true, our solution x = -8 is correct. Verification is a crucial step in problem-solving. It allows us to confirm the accuracy of our solution and identify any potential errors. By substituting the value back into the original equation, we can ensure that it satisfies the given conditions. This process reinforces our understanding of the equation and the solution. It also builds confidence in our problem-solving abilities. Verification is a valuable habit to develop, as it helps prevent mistakes and ensures the correctness of our answers. It's an essential part of the mathematical process and should not be overlooked. By taking the time to verify our solutions, we strengthen our understanding and improve our accuracy. This step is particularly important in more complex problems, where errors can be easily made. So, always remember to verify your solutions and ensure they are correct.
Conclusion
In conclusion, we have successfully solved the equation 13 - x = 21 and found that x = -8. We achieved this by using algebraic manipulation, which involved subtracting 13 from both sides of the equation and then multiplying both sides by -1. We also verified our solution by substituting it back into the original equation, confirming its accuracy. This exercise demonstrates the fundamental principles of solving linear equations, a crucial skill in algebra and mathematics in general. In conclusion, mastering these techniques will empower you to tackle a wide range of mathematical problems. The ability to solve for unknown variables is a cornerstone of mathematical proficiency. By understanding the steps involved and practicing regularly, you can develop confidence and accuracy in your problem-solving abilities. Remember, the key is to isolate the variable by performing inverse operations and maintaining the balance of the equation. This systematic approach, coupled with verification, ensures the correctness of your solutions. As you continue your mathematical journey, you'll encounter more complex equations, but the fundamental principles remain the same. So, embrace the challenge, practice diligently, and watch your problem-solving skills soar. This exercise serves as a solid foundation for further exploration in the world of mathematics.
