Solving The Equation: 3x - 5 = 3, Step-by-Step

Hey guys! Let's dive into a classic algebra problem today. We're going to break down how to solve the equation 3x - 5 = 3. It's super important to understand this stuff, whether you're just starting out in math or brushing up on your skills. We'll go through each step clearly, making sure everyone can follow along. This is the kind of problem that forms the foundation for more complex equations you'll encounter later on, so paying attention now will save you a lot of headaches down the road. I will make sure everything is crystal clear, so you can ace this problem. Ready to get started? Let's jump in!

Understanding the Basics: What Does This Equation Mean?

Alright, before we start solving, let's make sure we're all on the same page about what the equation 3x - 5 = 3 even means. Essentially, this equation is asking us: "What value of 'x' makes this statement true?" In other words, what number can we plug in for 'x' so that when we multiply it by 3 and then subtract 5, we get 3? The variable 'x' represents an unknown number that we're trying to figure out. Solving the equation is all about isolating 'x' – getting it by itself on one side of the equals sign. That’s the goal. Think of it like a balancing act; we need to do the same thing to both sides of the equation to keep it balanced. Every step we take is designed to get us closer to finding the value of 'x'. Now, let's break down each part, beginning with the constants and then addressing the operational functions and variable.

So, we have three components here: the term '3x', the constant '-5', and the constant '3' on the other side of the equals sign. The term '3x' means 3 multiplied by 'x'. The '-5' is a constant value subtracted from '3x'. The '3' on the right side is our target value. Our mission is to rearrange this equation until 'x' is all alone and equal to a number. Remember, the equal sign acts as the fulcrum, and we need to keep both sides balanced throughout the process. Each operation we perform must be applied to both sides to maintain that balance. Are you ready to get started? Let's do it. This process will help strengthen your fundamental skills and improve your ability to solve different types of algebraic equations. This will provide a solid foundation for more complex problems later on.

Step-by-Step Solution: Isolating the Variable

Okay, now let's get into the step-by-step process of solving the equation. We want to get 'x' by itself. The first step is to get rid of that '-5'. We do this by using the inverse operation, which in this case is adding 5 to both sides of the equation. Remember, we have to keep things balanced.

So, our original equation is: 3x - 5 = 3.

Add 5 to both sides: 3x - 5 + 5 = 3 + 5.

This simplifies to: 3x = 8.

See how adding 5 to both sides eliminated the -5 on the left? Now, we have a simpler equation, and we're one step closer to our goal. The principle here is that whatever you do on one side of the equation, you must do on the other side to maintain the balance. It's like a seesaw – if you only add weight to one side, the whole thing tips over. By adding 5 to both sides, we've kept the equation balanced while moving us closer to our final answer. Make sure you're taking it slow and double-checking each step as we go. And always remember, each step builds on the previous one, so understanding each step is key for moving forward with more complicated math problems in the future. Let's take a look at the next step.

Dividing Both Sides

Now that we have 3x = 8, the next step is to get 'x' completely alone. Currently, 'x' is being multiplied by 3. To undo that, we perform the inverse operation, which is to divide both sides of the equation by 3.

So we have: 3x = 8.

Divide both sides by 3: 3x / 3 = 8 / 3.

This simplifies to: x = 8/3.

And there you have it! We've isolated 'x' and found its value. So, x equals 8/3. This is the solution to the equation. This last step is crucial because it removes the coefficient (the number in front of the variable) and allows us to find the exact value of 'x'. At this point, 'x' is not being added, subtracted, or multiplied by any other values, so we can say that the equation is solved. Congratulations, guys! We have successfully solved this equation.

Verifying the Solution: Checking Your Work

It’s always a good idea to double-check your answer. This is super easy to do, and it ensures that you actually have the correct solution. We take our solution and plug it back into the original equation. If both sides of the equation are equal after you plug it in, then you know you've got it right!

Our solution is x = 8/3. Our original equation was 3x - 5 = 3.

Let's substitute 8/3 for x: 3 * (8/3) - 5 = 3.

Simplify: 8 - 5 = 3.

3 = 3.

Since the left side equals the right side, we know that our solution, x = 8/3, is correct! Congratulations, guys! You've not only solved the equation but also verified your answer to ensure its accuracy. That’s a great habit to build. Always double-check your answers when solving problems; it helps you catch mistakes early and reinforces your understanding. This verification step is fundamental to developing strong problem-solving habits in mathematics. You will find that it increases your confidence in solving complex problems, and prevents minor errors from leading to major mistakes later on.

Conclusion: Mastering the Basics

Alright, we did it, guys! We successfully solved the equation 3x - 5 = 3 and found that x = 8/3. You’ve taken the first big step in solving algebraic equations by understanding inverse operations, keeping equations balanced, and verifying your solution. Remember, the key to mastering algebra, and math in general, is practice. The more you solve these types of equations, the more comfortable and confident you’ll become. Start with simpler problems and gradually move on to more complex ones. Don't be afraid to make mistakes—they're a natural part of the learning process. Each time you solve a problem, you're reinforcing your skills and building a strong foundation for future math concepts. Embrace challenges, practice regularly, and celebrate your progress. Your hard work will definitely pay off, I promise. So, keep practicing, and you'll be well on your way to mastering algebra and beyond. Also, don’t forget to review what you’ve learned today! Try solving similar problems, and you'll be surprised how much easier it gets with practice. Keep it up, guys; I know you can do it!