Solving For R: A Simple Equation Explained

Let's break down how to solve the equation $r - 5 = 21$ for r. This is a fundamental algebra problem, and understanding how to solve it is crucial for more complex math later on. So, let's dive right in and make it super clear. Solving algebraic equations is a core skill in mathematics, applicable in various fields from science and engineering to finance and economics. Mastering these basics lays a strong foundation for tackling more complex problems and real-world applications. When students grasp the fundamental principles behind equation solving, they develop a logical and analytical mindset that extends beyond the classroom. Understanding how to manipulate equations helps in problem-solving, critical thinking, and decision-making processes. These skills are essential for success in higher education and professional careers. Think of it as building blocks: a solid understanding of algebra makes advanced topics like calculus and differential equations much easier to comprehend. It's not just about getting the right answer; it's about understanding the why and how behind each step. So, pay close attention, practice regularly, and don't hesitate to ask questions. With consistent effort, you'll find that solving equations becomes second nature, opening doors to a deeper appreciation and understanding of mathematics. Remember, mathematics is not just a subject but a tool that empowers you to analyze and solve problems in any domain. Keep practicing, and you'll see how these skills become invaluable in your life. Good luck!

Understanding the Equation

The equation we're dealing with is $r - 5 = 21$. What this means is that we have a variable, r, and when we subtract 5 from it, we get 21. Our goal is to isolate r on one side of the equation to find out what its value is. Isolating variables is a fundamental technique in algebra. It allows us to determine the specific value of an unknown quantity by manipulating the equation to get the variable alone on one side. This process involves using inverse operations to undo the operations that are applied to the variable. In this case, since 5 is being subtracted from r, we will add 5 to both sides of the equation to isolate r. Understanding this concept is essential for solving more complex equations in the future. It’s like detective work: you're trying to uncover the hidden value of r by carefully following the clues provided by the equation. Each step you take brings you closer to the solution, revealing the true value of the variable. The importance of mastering this skill cannot be overstated. It's the foundation upon which more advanced algebraic techniques are built. So, take your time, practice consistently, and make sure you understand the logic behind each step. This will not only help you solve equations more efficiently but also deepen your understanding of mathematics as a whole. And remember, every equation is a puzzle waiting to be solved!

Solving for r: Step-by-Step

To solve for r in the equation $r - 5 = 21$, we need to get r by itself on one side of the equation. We do this by performing the inverse operation. Since 5 is being subtracted from r, we add 5 to both sides of the equation. Here’s how it looks:

$r - 5 + 5 = 21 + 5$

This simplifies to:

$r = 26$

So, the value of r that makes the equation true is 26. Adding the same number to both sides of an equation maintains the equality, which is a core principle of algebraic manipulation. This step-by-step process ensures that we isolate the variable r without changing the equation's fundamental balance. It’s like using a balancing scale: whatever you do to one side, you must do to the other to keep it level. This principle is essential for solving any algebraic equation, no matter how complex. By carefully following each step and understanding the logic behind it, you can confidently solve for any variable. Remember, the goal is to isolate the variable, and you achieve this by performing inverse operations. Keep practicing, and you'll become a master of equation solving. And don't forget to check your work to ensure that your solution is correct. This will help you build confidence and avoid mistakes in the future. Happy solving!

Verification

To make sure our answer is correct, we can substitute the value we found for r back into the original equation. If the equation holds true, then we know we've solved for r correctly. Let's do that now:

Original equation: $r - 5 = 21$

Substitute $r = 26$:

$26 - 5 = 21$

$21 = 21$

Since the equation holds true, our solution r = 26 is correct. Verifying your solution is a crucial step in problem-solving. It ensures that you haven't made any mistakes along the way and that your answer is accurate. By substituting the value back into the original equation, you can quickly check if it satisfies the equation. This not only gives you confidence in your answer but also helps you catch any errors you might have made. Think of it as double-checking your work: it's always a good idea to make sure everything is correct before moving on. This practice will help you develop a strong sense of accuracy and attention to detail, which are valuable skills in any field. So, always remember to verify your solutions, and you'll become a more confident and successful problem solver. And remember, even the most experienced mathematicians make mistakes, so don't be afraid to double-check your work. It's a sign of a careful and thorough approach to problem-solving.

Conclusion

So, to wrap things up, we've successfully solved the equation $r - 5 = 21$ for r. By adding 5 to both sides of the equation, we isolated r and found that r = 26. Always remember to verify your answer to ensure accuracy. Great job, guys! Understanding how to solve simple algebraic equations like this is a foundational skill. It opens the door to more complex mathematical concepts and problem-solving techniques. By mastering these basics, you build a strong foundation for future learning and success. Keep practicing, and you'll find that solving equations becomes second nature. Remember, mathematics is not just a subject but a tool that empowers you to analyze and solve problems in any domain. Whether you're working on a science project, managing your finances, or designing a building, mathematical skills will always be valuable. So, embrace the challenge, keep learning, and never stop exploring the fascinating world of mathematics. And remember, every problem is an opportunity to learn and grow. So, keep solving, and you'll become a more confident and capable problem solver. Good luck on your mathematical journey!