Solving For Y: A Step-by-Step Guide
Hey guys! Let's dive into the world of algebra and learn how to solve for y in the equation y + 5y = 24. It sounds complicated, but trust me, it's a piece of cake once you understand the basic steps. This guide will break down the process into easy-to-follow instructions, ensuring you grasp the concept and can tackle similar problems with confidence. We'll simplify the equation, isolate the variable, and find the value of y. So, grab your pencils, and let's get started on this exciting mathematical journey. Solving for y is a fundamental skill in algebra, and mastering it opens doors to understanding more complex equations and problem-solving strategies. We'll start with the basics, ensuring everyone is on the same page, and gradually move towards the solution. This process will not only teach you how to solve this specific equation but will also equip you with the skills to solve a wide range of algebraic problems. The ability to manipulate and solve equations is crucial in various fields, from science and engineering to economics and computer science. Therefore, understanding the fundamentals of solving for variables is an incredibly valuable skill. We'll be using clear and concise language, ensuring that the concepts are accessible to everyone, regardless of their prior experience with algebra. Remember, practice is key, so don't hesitate to work through the examples and try some additional problems on your own. Let's make this fun and educational!
Step 1: Combining Like Terms
Alright, the first step in solving our equation, y + 5y = 24, is to combine like terms. The beauty of this equation is that we already have like terms on one side. Both y and 5y are terms that contain the variable y. To combine them, think of it like adding apples. If you have 1 apple and you add 5 more apples, how many apples do you have? You have 6 apples. In the same way, y + 5y equals 6y. So, the equation simplifies to 6y = 24. See? That wasn't so hard, right? Combining like terms is a foundational concept in algebra, and it significantly simplifies equations, making them easier to solve. When dealing with more complex equations, combining like terms is often the first and most crucial step in streamlining the problem. Remember, like terms are terms that have the same variable raised to the same power. For instance, 3x and 7x are like terms, while 3x and 3x² are not. Always be mindful of the signs (+ or -) in front of the terms, as they determine whether you add or subtract. This step sets the stage for isolating the variable and ultimately finding its value. Practice makes perfect, and with consistent effort, you'll become a pro at combining like terms. This skill extends beyond just solving equations; it’s an essential component of mathematical problem-solving in general. Understanding how to group and simplify terms is a crucial part of becoming proficient in algebra and opens the doors to more complex mathematical endeavors. Let's move on to the next step, where we'll isolate y.
Step 2: Isolating the Variable
Now that we've simplified our equation to 6y = 24, our goal is to isolate the variable y. To do this, we need to get y all by itself on one side of the equation. Currently, y is being multiplied by 6. To undo this multiplication, we need to perform the opposite operation, which is division. We'll divide both sides of the equation by 6. This is super important because whatever you do to one side of the equation, you must do to the other side to keep the equation balanced. So, dividing both sides by 6, we get: (6y) / 6 = 24 / 6. On the left side, the 6s cancel out, leaving us with just y. On the right side, 24 divided by 6 equals 4. Thus, we've successfully isolated y and our equation now reads y = 4. Great job, we're almost there! Isolating the variable is a critical step in solving equations. It involves performing inverse operations to get the variable by itself. Remember, the key is to maintain the balance of the equation by applying the same operation to both sides. Mastering this technique allows you to solve a wide variety of equations, from simple linear equations to more complex algebraic expressions. When isolating a variable, you need to consider the operations being performed on it. Is it being added, subtracted, multiplied, or divided? Then, you apply the inverse operation. For example, if the variable is being added to a number, subtract that number from both sides. If it's being multiplied, divide both sides. This process may seem tricky at first, but with practice, it will become second nature. Remember to always double-check your work to ensure you've performed the operations correctly and that your solution is valid. Let's move on to the next step. It's the last one!
Step 3: The Solution
Congratulations, guys! We've reached the final step, and we've successfully solved for y! As we determined in Step 2, the equation y = 4 is the solution to our original equation, y + 5y = 24. This means that the value of y that satisfies the equation is 4. You can even check your answer by substituting 4 back into the original equation to see if it holds true. If you substitute 4 for y, you get 4 + 5(4) = 24, which simplifies to 4 + 20 = 24. Since 24 = 24, our solution is correct! That's how we know we've got the right answer! Solving for a variable is a fundamental skill in algebra, enabling you to find unknown values within an equation. By mastering these steps, you will now be able to confidently solve equations like this one. Remember, the key to success in algebra is understanding the basic principles and practicing regularly. Don't be discouraged if you encounter difficulties along the way. Every challenge is an opportunity to learn and grow. Keep practicing, and you'll become proficient at solving algebraic equations in no time. The ability to solve for variables is applicable in various fields, so well done on mastering this skill! Always double-check your answer to be sure it makes sense in the context of the original problem. This habit ensures accuracy and builds your confidence in your problem-solving abilities. Practice different types of equations to reinforce your understanding and become more comfortable with different scenarios. You've got this!
Conclusion
We've successfully solved for y in the equation y + 5y = 24, and the answer is y = 4. We did it by combining like terms, isolating the variable, and then solving for its value. I hope this step-by-step guide has been helpful! Remember, the more you practice, the easier it will become. Keep up the great work! Algebraic equations are the building blocks of mathematics and are used extensively in many different fields. The ability to manipulate and solve these equations is a crucial skill. The key to mastering this is practice and persistence. Keep challenging yourself, and you’ll continue to improve your skills. Embrace the challenges; they are opportunities to develop your mathematical thinking. Keep practicing, and you'll find that solving equations becomes more manageable with each attempt. Keep up the enthusiasm, and enjoy the process of learning.
