Solve For Y: Y - 92 = -21 Equation Made Easy

Hey guys! Let's dive into solving a simple algebraic equation today. We're going to tackle the problem y - 92 = -21 and figure out what value of 'y' makes this equation true. Don't worry, it's easier than it looks! We'll break it down step-by-step so everyone can follow along. Solving for variables is a fundamental skill in mathematics, so mastering this will set you up for success in more complex problems later on. Think of it as building a strong foundation for your math journey. We'll not only find the answer but also understand why we're doing each step. This conceptual understanding is key to truly grasping algebra. So, grab your pencils and let's get started! Remember, math is a journey, not a race. It's about understanding the process, not just getting the answer. So, let's embark on this journey together and unlock the secrets of algebra, one equation at a time. This equation is a great starting point because it introduces the core concept of isolating a variable, which is the cornerstone of solving algebraic equations. We will be using the addition property of equality to isolate 'y' on one side of the equation. This property states that adding the same value to both sides of an equation maintains the equality. By adding 92 to both sides of the equation, we'll effectively eliminate the -92 from the left side, leaving 'y' by itself. This principle is fundamental and applies to a wide range of algebraic problems, so understanding it well is crucial. As we progress, you'll see how this simple technique can be adapted to solve more complex equations involving multiple operations and variables. So, pay close attention to each step, and don't hesitate to ask questions if anything is unclear. Let's make math fun and approachable together!

Understanding the Equation: y - 92 = -21

Before we jump into solving, let's make sure we understand what the equation y - 92 = -21 actually means. In simple terms, it's saying: "There's a number (we're calling it 'y') and if you subtract 92 from it, you get -21." Our mission is to find out what that number 'y' is. Think of 'y' as a mystery box, and our goal is to open the box and see what's inside. Equations are like puzzles, and solving them is like putting the pieces together to reveal the hidden solution. The beauty of algebra is that it gives us the tools to systematically solve these puzzles. We're not just guessing; we're using logical steps to arrive at the correct answer. This equation involves a single variable ('y') and a single operation (subtraction). This makes it a perfect starting point for understanding how to isolate variables, which is the core concept in solving algebraic equations. The equal sign (=) is the heart of the equation. It tells us that the expression on the left side (y - 92) has the same value as the expression on the right side (-21). Maintaining this equality is crucial as we manipulate the equation to solve for 'y'. Any operation we perform must be applied to both sides to keep the equation balanced. This is a fundamental principle in algebra and is often visualized as a balanced scale. If you add or subtract weight from one side, you must do the same to the other side to maintain the balance. So, with this understanding in mind, let's move on to the actual solving process. We'll use a simple but powerful technique to isolate 'y' and reveal its value. Remember, the key is to keep the equation balanced and apply operations strategically to simplify it. Math is all about logic and consistency, and by following these principles, we can confidently solve a wide range of problems.

Step-by-Step Solution: Isolating 'y'

Okay, let's get down to business and solve for 'y' in the equation y - 92 = -21. Our main goal here is to get 'y' all by itself on one side of the equation. This is what we mean by isolating the variable. To do this, we need to get rid of the '- 92' that's hanging out with 'y'. The way we do that is by using the inverse operation. The inverse operation of subtraction is addition. So, we're going to add 92 to both sides of the equation. Remember, whatever we do to one side, we must do to the other to keep the equation balanced. It's like a seesaw; if you add weight to one side, you need to add the same weight to the other side to keep it level. Here's how it looks:

y - 92 + 92 = -21 + 92

Now, let's simplify. On the left side, '-92 + 92' cancels each other out, leaving us with just 'y'. On the right side, we have '-21 + 92', which equals 71. So, our equation now looks like this:

y = 71

And there you have it! We've successfully isolated 'y' and found its value. The solution to the equation y - 92 = -21 is y = 71. It's like we've opened the mystery box and found that it contains the number 71. But we're not done yet! It's always a good idea to check our answer to make sure we didn't make any mistakes along the way. This is a crucial step in problem-solving, as it gives us confidence in our solution. So, let's move on to the next step and verify our answer. Remember, math is not just about finding the answer; it's about understanding the process and being confident in our results. By checking our work, we're reinforcing our understanding and developing good problem-solving habits.

Checking Our Answer: y = 71

Alright, guys, we've found that y = 71 is the solution to our equation. But, like any good detectives, we need to verify our findings! Checking our answer is super important because it helps us catch any little mistakes we might have made along the way. It's like double-checking your work before submitting it, just to be sure everything is perfect. To check our answer, we're going to plug the value we found for 'y' (which is 71) back into the original equation: y - 92 = -21. So, we'll replace 'y' with 71 and see if the equation holds true.

Here's how it looks:

71 - 92 = -21

Now, let's simplify the left side of the equation. 71 - 92 is equal to -21. So, our equation now looks like this:

-21 = -21

Boom! The left side of the equation is equal to the right side. This means our solution, y = 71, is correct! We've successfully solved the equation and verified our answer. It's like completing a puzzle and seeing all the pieces fit perfectly together. Checking our answer not only confirms that we've found the correct solution but also reinforces our understanding of the equation and the steps we took to solve it. It's a great way to build confidence in our mathematical abilities. So, always remember to check your answers whenever possible. It's a valuable habit that will serve you well in all your mathematical endeavors. We've solved for 'y', understood the equation, and verified our solution. Now, let's take a step back and reflect on what we've learned.

Conclusion: Mastering the Basics

Great job, everyone! We've successfully solved the equation y - 92 = -21 and found that y = 71. We not only found the answer but also understood the process behind it. We learned about isolating variables, using inverse operations, and the importance of checking our answers. These are fundamental skills in algebra, and mastering them will open doors to solving more complex problems. Remember, math is like building a house. You need a strong foundation to build something great. And the skills we've practiced today are some of the essential building blocks for your mathematical foundation. Solving equations is not just about getting the right answer; it's about developing logical thinking and problem-solving skills. These skills are valuable not only in math but also in everyday life. From planning a budget to making decisions, the ability to think logically and solve problems is crucial. So, keep practicing, keep exploring, and keep asking questions. The more you engage with math, the more confident and capable you'll become. This particular equation was a simple example, but the principles we've applied can be used to solve a wide range of algebraic problems. The key is to break down the problem into smaller steps, understand the underlying concepts, and apply the appropriate techniques. And don't forget the importance of checking your answers! It's a small step that can make a big difference. So, congratulations on mastering this equation! You've taken another step forward on your mathematical journey. Keep up the great work, and remember, math can be fun and rewarding when you approach it with curiosity and a willingness to learn.