Solving 7x4+ (9x7-57)-18+2 A Step-by-Step Guide

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Hey guys! Ever stumbled upon a math problem that looks like a jumbled mess of numbers and operations? Don't worry, we've all been there! Today, we're going to break down a seemingly complex equation and solve it together, step by step. Our mission, should we choose to accept it, is to solve: >7x4+ (9x7-57)-18+2. Sounds intimidating? Nah, we've got this! We'll make it super easy and fun. Let's dive in!

Understanding the Order of Operations

Before we jump into the nitty-gritty, it’s super important to understand the order of operations. Think of it as the golden rule of math – you gotta follow it! Otherwise, you might end up with the wrong answer, and nobody wants that, right? The order of operations is often remembered by the acronym PEMDAS, which stands for:

  • Parentheses
  • Exponents
  • Multiplication and Division (from left to right)
  • Addition and Subtraction (from left to right)

Why is PEMDAS so crucial? Imagine trying to bake a cake without following the recipe's order. You might add the flour before the eggs, and boom, you've got a lumpy mess! Math is similar; the order in which you perform operations drastically affects the outcome. So, keep PEMDAS in your mental toolbox—it's your best friend in solving equations!

Now, let’s break down each part of PEMDAS a bit further so we’re all on the same page. Think of Parentheses as VIP sections in a math problem. Anything inside them gets special treatment and is calculated first. This is because parentheses group numbers and operations together, indicating they should be treated as a single unit. Next up are Exponents, those little numbers hanging out in the top right corner. They tell you how many times to multiply a number by itself. For example, 2^3 (2 to the power of 3) means 2 * 2 * 2, which equals 8. Exponents give numbers a growth spurt, so they're calculated early in the game.

Moving on, we have Multiplication and Division. These two are like partners in crime, and they share the same level of priority. When you see them in an equation, you tackle them from left to right. It’s like reading a sentence; you don’t jump around, you go in order. Similarly, Addition and Subtraction are the final duo. They also share the same priority and are tackled from left to right. Once you've handled the parentheses, exponents, multiplication, and division, you're left with these two, which bring you to the finish line.

Understanding PEMDAS is more than just memorizing an acronym; it's about grasping the logic behind the structure of mathematical expressions. By following this order, we ensure that our calculations are consistent and accurate. So, as we approach our main problem, keep PEMDAS in mind. It's the roadmap that will guide us to the correct solution. With this fundamental knowledge, we can confidently tackle even the most daunting-looking equations. Let's get back to our problem now, and see how PEMDAS helps us crack it!

Step 1: Tackling the Parentheses

Alright, let's get our hands dirty! Remember PEMDAS? First up: Parentheses. Our equation is >7x4+ (9x7-57)-18+2. Notice those curved brackets? That's our starting point. Inside the parentheses, we have 9x7-57. Now, even within the parentheses, we need to follow the order of operations. So, what comes first? Multiplication or subtraction? You guessed it—multiplication!

We start by calculating 9 multiplied by 7. If you're a multiplication whiz, you already know the answer. If not, no worries! Let's break it down. 9 times 7 is 63. So, we've conquered the first part inside the parentheses. Our equation now looks like this: >7x4+ (63-57)-18+2. See how we've simplified things already? We're making progress!

Now, we still have something to resolve inside the parentheses: 63-57. This is a straightforward subtraction. What do we get when we subtract 57 from 63? The answer is 6. Excellent! We've now completely cleared the parentheses. Our equation is shaping up nicely and looks like this: >7x4+ 6-18+2. Feels much more manageable, doesn't it? By focusing on the parentheses first, we've reduced the complexity and set ourselves up for the next steps. Remember, breaking down a problem into smaller, manageable chunks is key to solving it effectively. And that’s exactly what we’re doing here.

The importance of tackling parentheses first can't be overstated. They act as a container, grouping operations that need to be resolved as a unit before interacting with the rest of the equation. This ensures the integrity of the mathematical expression and prevents errors. By prioritizing parentheses, we maintain the correct order and pave the way for accurate calculations. So, give yourself a pat on the back! You've successfully navigated the first hurdle, and we're one step closer to solving the entire equation. Let's keep this momentum going as we move on to the next step. Onwards and upwards, mathletes! We're turning this complex equation into a piece of cake, one step at a time.

Step 2: Multiplication Comes Next

Great job on conquering the parentheses, guys! We're rolling now! So, what's next on our PEMDAS checklist? That's right, it's Multiplication and Division. Looking at our simplified equation, >7x4+ 6-18+2, we can spot a multiplication operation right away. It's 7 multiplied by 4. Let's tackle that head-on!

What's 7 times 4? If you know your times tables, you'll immediately shout out 28! If you're still working on them, that's totally cool too. You can always add 7 four times (7+7+7+7) or use a calculator to double-check. Either way, 7 multiplied by 4 is indeed 28. So, we replace 7x4 with 28 in our equation. Now it looks like this: >28+ 6-18+2. See how each step makes the equation simpler and less intimidating? We're chipping away at it like pros!

Why do we prioritize multiplication (and division) over addition and subtraction? It's all about the underlying mathematical principles. Multiplication is essentially a shortcut for repeated addition. By performing multiplication first, we're consolidating these repeated additions into a single term, which helps streamline the equation. It's like taking a shortcut on a journey—you reach your destination faster and more efficiently. This step is crucial in ensuring that we follow the correct mathematical logic and arrive at the accurate solution. Ignoring this step would be like mixing up ingredients in a recipe, potentially leading to a mathematical disaster!

With the multiplication out of the way, our equation is becoming increasingly clear. We've transformed a potentially confusing expression into a straightforward sequence of additions and subtractions. This is the beauty of following the order of operations—it provides a clear roadmap, guiding us through the complexities of mathematical expressions. Each step we take is a step closer to the final answer, and with multiplication now handled, we're well on our way. So, give yourselves another pat on the back! You've aced the multiplication step, and we're ready to move on to the final leg of our journey. Let's keep the momentum going as we tackle the remaining additions and subtractions. Onward, math whizzes!

Step 3: Adding and Subtracting (Left to Right)

Alright, champions! We've made it to the final stretch. We've conquered the parentheses, tamed the multiplication, and now we're left with the dynamic duo: Addition and Subtraction. Remember, these operations have equal priority, so we tackle them in the order they appear, moving from left to right. Our equation is now sitting pretty at >28+ 6-18+2. Let's finish strong!

First up, we have 28 plus 6. Easy peasy, right? 28 + 6 equals 34. So, we replace 28+6 with 34. Our equation now transforms into: >34-18+2. We're cruising through this! Notice how we're taking it one step at a time, keeping everything neat and organized. This helps prevent those sneaky little errors that can creep in when we rush.

Next in line is 34 minus 18. Time for a little subtraction action! What's 34 - 18? If you need to, you can borrow from the tens place or use your fingers—whatever works for you! The answer is 16. Fantastic! Our equation is getting even simpler: >16+2. We're almost there, guys! Can you feel the mathematical victory in the air?

Finally, we have 16 plus 2. This is the home stretch! What's 16 + 2? It's 18! Woohoo! We've done it! We've successfully navigated all the operations and arrived at our final answer. Our equation, which once looked like a tangled mess, has been tamed and simplified, thanks to our understanding of PEMDAS and our step-by-step approach. This final stage, where we handle addition and subtraction from left to right, is crucial for ensuring accuracy. Just like in a relay race, each step is essential, and the order matters. By carefully performing each addition and subtraction, we avoid any mix-ups and arrive at the correct solution.

So, let's recap our journey. We started with a seemingly complex equation, >7x4+ (9x7-57)-18+2, and through the power of PEMDAS and a methodical approach, we've broken it down into manageable chunks. We conquered the parentheses, mastered the multiplication, and elegantly handled the addition and subtraction. And what did we get? We arrived at our final answer: 18! Give yourselves a huge round of applause! You've demonstrated your math prowess and shown that even the most intimidating equations can be solved with the right strategy and a little bit of perseverance. Remember, math is like a puzzle, and each piece fits perfectly when you follow the rules. And now, you've added another puzzle-solving skill to your repertoire. Congratulations, mathletes! You've nailed it!

Final Answer: 18

So, there you have it! By following the order of operations (PEMDAS) and breaking down the problem into smaller, manageable steps, we've successfully solved the equation >7x4+ (9x7-57)-18+2. The answer is 18! High fives all around! Remember, math isn't about being a genius; it's about understanding the rules and applying them step by step. You guys rock!