Solving For B: B/3 + 7.26 = 10.96 - A Step-by-Step Guide

Hey guys! Today, we're diving into a common math problem: solving for a variable. In this case, we're going to figure out the value of 'b' in the equation b/3 + 7.26 = 10.96. Don't worry, it's not as scary as it looks! We'll break it down step-by-step so you can conquer similar problems with confidence. Whether you're a student tackling algebra or just brushing up on your math skills, this guide will provide a clear and easy-to-follow method to find the solution. We'll go through each step meticulously, explaining the reasoning behind each operation, so you not only get the answer but also understand why it's the answer. So, let's put on our math hats and get started on this algebraic adventure! Remember, practice makes perfect, so feel free to try out these techniques on other equations as well. By the end of this guide, you'll be well-equipped to handle equations of this type and impress your friends with your math skills. Let's jump right in and unlock the mystery of solving for 'b'! This journey into the world of equations will be both informative and empowering, so let's make the most of it. Are you ready? Let's go!

1. Understanding the Equation

Before we jump into solving, let's make sure we understand what the equation is telling us. b/3 + 7.26 = 10.96 means that if you take the value of 'b', divide it by 3, and then add 7.26, you'll get 10.96. Our goal is to isolate 'b' on one side of the equation so we can see exactly what its value is. Think of it like a puzzle – we need to undo the operations that are being done to 'b' to reveal its true identity. The beauty of algebra lies in this very process of unraveling the unknowns. Each step we take is like peeling back a layer to get closer to the core. So, let's approach this with a clear understanding of our objective: to get 'b' all by itself on one side of the equals sign. Once we achieve that, we'll have successfully solved the equation and found the value of 'b'. Remember, it's all about reversing the operations in the correct order. We'll start by dealing with the addition, and then we'll tackle the division. This methodical approach will help us navigate through the equation and arrive at the correct solution with ease. Are you ready to dive into the first step of our algebraic journey? Let's do it!

2. Isolating the Term with 'b'

The first step in solving for 'b' is to isolate the term that contains 'b', which is b/3. To do this, we need to get rid of the + 7.26 on the left side of the equation. Remember, whatever we do to one side of the equation, we must do to the other side to keep it balanced. It's like a see-saw; if you take weight off one side, you need to take the same weight off the other to keep it level. So, to remove the + 7.26, we'll subtract 7.26 from both sides of the equation. This gives us:

b/3 + 7.26 - 7.26 = 10.96 - 7.26

Simplifying this, we get:

b/3 = 3.7

Now, we're one step closer! We've successfully isolated the term with 'b' on one side of the equation. This is a crucial step because it sets us up for the final operation that will reveal the value of 'b'. Think of it as clearing the path to our destination. By removing the + 7.26, we've made it much easier to see what needs to be done next. The equation is becoming cleaner and more manageable, and we're gaining momentum towards the solution. Remember, each step in algebra is a building block, and this one is a significant one. We've effectively simplified the equation and positioned ourselves perfectly for the final act. Are you excited to see what's next? Let's move on and finish this!

3. Solving for 'b'

We're almost there! We have b/3 = 3.7. Now, 'b' is being divided by 3. To undo this division and isolate 'b', we need to multiply both sides of the equation by 3. This is the reverse operation of division, and it's exactly what we need to free 'b' from the fraction. Again, we're maintaining balance by doing the same thing to both sides. This gives us:

(b/3) * 3 = 3.7 * 3

On the left side, the multiplication by 3 cancels out the division by 3, leaving us with just 'b'. On the right side, 3.7 multiplied by 3 equals 11.1. So, we have:

b = 11.1

And there you have it! We've solved for 'b'. The value of 'b' that makes the equation true is 11.1. This is the moment of triumph when all our hard work pays off. We've successfully navigated the equation, step by step, and arrived at the solution. It's a great feeling, isn't it? This process of isolating the variable and undoing the operations is the core of solving algebraic equations. And now you've mastered it! Remember, the key is to stay organized, keep the equation balanced, and perform the correct operations in the correct order. With practice, you'll become a pro at solving for any variable. But for now, let's celebrate our success in finding the value of 'b'. We did it!

4. Checking Your Answer

It's always a good idea to check your answer to make sure it's correct. To do this, we'll substitute our solution, b = 11.1, back into the original equation: b/3 + 7.26 = 10.96. So, we have:

11.1 / 3 + 7.26 = 10.96

First, we divide 11.1 by 3, which equals 3.7. So the equation becomes:

3.7 + 7.26 = 10.96

Now, we add 3.7 and 7.26, which indeed equals 10.96. So, our equation is true!

10.96 = 10.96

This confirms that our solution, b = 11.1, is correct. Checking your answer is like the final seal of approval on your work. It gives you the confidence to know that you've not only found a solution but also that it's the right solution. It's a simple step, but it can save you from making mistakes and ensure that you're on the right track. So, always remember to plug your answer back into the original equation and verify that it holds true. It's a best practice that will serve you well in all your mathematical endeavors. And in this case, it's given us the satisfaction of knowing that we've solved for 'b' accurately and completely. Well done!

Conclusion

So, we've successfully solved for 'b' in the equation b/3 + 7.26 = 10.96, and we found that b = 11.1. We walked through each step, from understanding the equation to isolating the variable and checking our answer. Solving algebraic equations like this is a fundamental skill in mathematics, and you've now added another tool to your math toolbox! Remember, the key is to break down the problem into smaller, manageable steps, stay organized, and always check your work. Practice makes perfect, so keep solving equations, and you'll become a master in no time. If you found this guide helpful, share it with your friends and keep exploring the fascinating world of mathematics. There's always something new to learn and discover! Congratulations on solving for 'b', and keep up the great work! You're well on your way to becoming a math whiz. And remember, math isn't just about numbers and equations; it's about problem-solving, critical thinking, and building a strong foundation for all kinds of challenges in life. So, embrace the journey, enjoy the process, and keep those mathematical muscles flexing! We're so proud of you for tackling this equation and coming out on top. Now, go forth and conquer more mathematical mountains!