Solving X*9+360=450 Equation For 4th Grade Students

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Hey there, fourth graders! Feeling a little puzzled by equations like x*9+360=450? No worries, we're here to break it down and make it super easy to understand. Think of it like a puzzle – we just need to find the missing piece, which in this case is our 'x'. So, let's dive in and solve this algebra problem together, step by step. Understanding the basics of algebra at this stage can build a strong foundation for future math adventures. Equations might seem intimidating at first, but once you grasp the underlying concepts, you'll see they are just logical puzzles waiting to be solved. This particular equation involves a combination of multiplication and addition, and we'll learn how to tackle each operation in the correct order. Remember, math is like building with LEGO bricks; each concept builds upon the previous one, so mastering these early skills is crucial. Our goal isn't just to find the answer but also to understand why we do each step. This way, you'll be able to apply these principles to all sorts of equations. And guess what? Solving equations is not just for math class! It's a skill that helps in everyday life, from figuring out how much change you'll get at the store to planning how to divide snacks among your friends. So, let's put on our thinking caps and embark on this exciting math journey together!

Understanding the Equation x*9+360=450

Okay, let's get started! Our equation is x*9+360=450. The first thing we need to do is understand what this equation is telling us. It's basically saying that if we multiply a number (that's our 'x') by 9, and then add 360 to the result, we should end up with 450. Think of 'x' as a secret number we need to uncover. This is the core of what algebra is about – finding those hidden values that make the equation true. In this case, the equation has two main operations: multiplication (x multiplied by 9) and addition (adding 360). We also have a total (450), which is the result we're aiming for. Before we start solving, it's good to get a feel for the numbers. We know we're looking for a value of 'x' that, when multiplied by 9, won't make the number so big that adding 360 gets us way over 450. This kind of estimation can be a helpful way to check our answer later. Remember, equations are like a balance scale. Whatever we do on one side, we have to do on the other side to keep the scale balanced. This idea of maintaining balance is super important when we're solving for 'x'. So, let's keep this balance scale in mind as we move through the steps. Now, let's move on to the next part: figuring out the best way to isolate our 'x'.

Step 1: Isolating the Term with 'x'

The key to solving this equation, and many others, is to get our 'x' all by itself on one side of the equals sign. This is called isolating the variable. To do this, we need to undo the operations that are happening to 'x'. Remember, we have x9+360=450. Right now, 'x' is being multiplied by 9, and then 360 is being added. To isolate 'x', we need to tackle these operations in reverse order. Think of it like unwrapping a present – you need to undo the last thing that was done first. So, instead of dealing with the multiplication right away, we're going to focus on getting rid of that +360. To do this, we use the opposite operation. The opposite of adding 360 is subtracting 360. Remember the balance scale? If we subtract 360 from the left side of the equation, we must subtract 360 from the right side as well to keep things balanced. This gives us a new equation: x9 + 360 - 360 = 450 - 360. Now, let's simplify. On the left side, +360 and -360 cancel each other out, leaving us with just x9. On the right side, 450 - 360 equals 90. So, our equation is now much simpler: x9 = 90. We're one step closer to finding 'x'! You can see how focusing on one operation at a time makes the problem much more manageable. Next, we'll deal with the multiplication to finally reveal our secret number.

Step 2: Solving for 'x'

Great job so far, guys! We've simplified our equation to x9 = 90. Now, we just need to get that 'x' all by itself. Right now, 'x' is being multiplied by 9. To undo multiplication, we use the opposite operation: division. So, we need to divide both sides of the equation by 9. Remember, keeping the balance is key! If we divide the left side by 9, we must divide the right side by 9 as well. This gives us: (x9) / 9 = 90 / 9. Let's simplify this. On the left side, dividing (x*9) by 9 just leaves us with 'x'. That's exactly what we wanted! On the right side, 90 divided by 9 is 10. So, we have our answer: x = 10! We've solved for 'x'! It means that the secret number that makes our original equation true is 10. To be absolutely sure, it's always a good idea to check our answer. We can do this by plugging 10 back into the original equation and seeing if it works. This step helps catch any little mistakes and gives us confidence in our solution. Let's head to the next section to do just that.

Step 3: Checking Your Answer

Alright, we think x = 10, but let's make absolutely sure! Checking our answer is like double-checking our work on a puzzle – we want to be 100% certain we got it right. To check, we're going to take our value for 'x' (which is 10) and plug it back into the original equation: x*9 + 360 = 450. So, we replace 'x' with 10, which gives us: 10 * 9 + 360 = 450. Now, we need to follow the order of operations (remember PEMDAS or BODMAS?). First, we do the multiplication: 10 * 9 = 90. So our equation now looks like this: 90 + 360 = 450. Next, we do the addition: 90 + 360 = 450. And guess what? 450 = 450! The equation is true! This means that our answer of x = 10 is correct. High five! Checking your work like this might seem like an extra step, but it's a super important habit to get into. It helps you avoid simple mistakes and builds confidence in your math skills. Plus, it's a great way to reinforce what you've learned. Now that we've successfully solved and checked our equation, let's recap the steps we took and talk about how you can apply these skills to other problems.

Recap and Tips for Solving Equations

Awesome job, everyone! We've conquered the equation x*9 + 360 = 450 and found that x = 10. Let's quickly recap the steps we took so you can tackle similar problems in the future:

  1. Understand the Equation: We started by making sure we understood what the equation was asking us to do. We identified the variable ('x'), the operations (multiplication and addition), and the goal (finding the value of 'x' that makes the equation true).
  2. Isolate the Term with 'x': We used inverse operations to start getting 'x' by itself. We subtracted 360 from both sides of the equation to undo the addition.
  3. Solve for 'x': We continued using inverse operations to isolate 'x' completely. We divided both sides of the equation by 9 to undo the multiplication.
  4. Check Your Answer: We plugged our solution (x = 10) back into the original equation to make sure it worked. This step is crucial for catching errors and building confidence.

Now, let's talk about some tips for solving equations in general. First, always remember the balance scale analogy. Whatever you do to one side of the equation, you must do to the other side. Second, work backwards through the order of operations. Undo addition and subtraction before multiplication and division. Third, show your work! Writing down each step makes it easier to track your progress and spot mistakes. Fourth, check your answer every time. It's the best way to be sure you've got it right. Finally, practice, practice, practice! The more equations you solve, the better you'll become at it. Solving equations is a fundamental skill in math, and it's a skill you'll use throughout your academic journey and beyond. Keep up the great work, and you'll be solving even more complex problems in no time! And remember, math can be fun when you approach it step by step and break it down into manageable pieces.