Solving [-(4-9)+(-5+8)]+(6-7): A Step-by-Step Guide

Hey guys! Today, we're going to break down a math problem that might look a little intimidating at first glance: [-(4-9)+(-5+8)]+(6-7). Don't worry, we'll tackle it together step-by-step so you can see how easy it really is. Math problems like this one involve the order of operations, which is crucial for getting the correct answer. We'll use the PEMDAS/BODMAS method to guide us through the solution. PEMDAS stands for Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). BODMAS is another acronym that stands for Brackets, Orders, Division and Multiplication (from left to right), Addition and Subtraction (from left to right). Both PEMDAS and BODMAS represent the same order of operations. Understanding this order is the key to success in solving mathematical expressions accurately. So, let’s jump right in and make sure we understand every single step. We'll go slow, we'll be thorough, and before you know it, you'll be solving problems like this in your sleep! Let's get started and demystify this equation together.

Understanding the Order of Operations (PEMDAS/BODMAS)

Before we even think about touching the actual numbers, let's quickly revisit the order of operations, often remembered by the acronyms PEMDAS or BODMAS. This is our golden rule in math, ensuring we all solve equations the same way and arrive at the same answer. Think of it as the recipe for a perfect mathematical cake – you wouldn't add the frosting before baking, right? PEMDAS/BODMAS tells us the exact order in which to perform operations: Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). This order ensures that we simplify expressions correctly and avoid any confusion. Ignoring this order can lead to incorrect answers, so it's essential to follow it consistently. For example, if we were to add before multiplying, we would end up with a completely different result. Mastering the order of operations is crucial for success in algebra and beyond. Understanding PEMDAS/BODMAS is like having a secret weapon in your math arsenal. It helps break down complex problems into manageable steps, making them much easier to solve. So, always remember to follow the order: Parentheses first, then exponents, followed by multiplication and division (from left to right), and finally, addition and subtraction (from left to right). This systematic approach will help you tackle any mathematical expression with confidence and accuracy. So, let's keep this in mind as we move forward and solve our problem step by step.

Step 1: Solving Inside the Parentheses

Okay, following PEMDAS, the first thing we need to tackle is what's inside the parentheses (or brackets, if you're a BODMAS fan!). We have two sets of parentheses in our problem: (4-9) and (-5+8). Let's take them one at a time. First up, (4-9). This is simply 4 minus 9, which gives us -5. Think of it like starting at 4 on the number line and moving 9 spaces to the left. Now, let's move on to the second set of parentheses: (-5+8). This is -5 plus 8, which equals 3. Imagine you owe someone 5 dollars, but you have 8 dollars – you pay them back and have 3 dollars left. See? Not so scary! By solving the operations inside the parentheses first, we've already simplified the problem quite a bit. This step is crucial because it reduces the complexity of the equation, making it easier to manage. Without simplifying the parentheses first, we could easily make mistakes in the subsequent steps. So, always remember to start with the parentheses – they are the gateway to simplifying the entire expression. This careful approach ensures that we maintain accuracy throughout the process and arrive at the correct solution. Now that we've handled the parentheses, we can move on to the next step in our mathematical journey. We're making great progress, guys! Keep up the awesome work!

Step 2: Dealing with the Negative Sign Outside the Parentheses

Alright, we've conquered the inside of the parentheses! Now our equation looks like this: [-(-5)+(3)]+(6-7). Notice that negative sign chilling outside the first set of parentheses? We gotta deal with that! This is where things can get a little tricky, but stick with me. The negative sign in front of the parentheses essentially means we're multiplying the entire expression inside the parentheses by -1. So, -(-5) becomes -1 * -5, which equals 5. Remember, a negative times a negative equals a positive! This is a fundamental rule in math that you'll use all the time. It's super important to get this down. Now our equation is looking even cleaner: [5+(3)]+(6-7). See how much simpler it's becoming? This step highlights the importance of understanding the rules of negative numbers. A simple negative sign can change the entire outcome if not handled correctly. So, always pay close attention to these signs and make sure to apply the rules consistently. This attention to detail will help you avoid common mistakes and ensure accuracy in your calculations. By addressing the negative sign outside the parentheses, we've taken another significant step towards simplifying the expression. We're breaking it down piece by piece, making it much more manageable. Keep going, guys! You're doing fantastic!

Step 3: Simplifying the Remaining Parentheses/Brackets

Excellent work, everyone! We're cruising right along. Our equation now reads: [5+(3)]+(6-7). We still have some parentheses to tackle, so let's keep following PEMDAS/BODMAS. First, let's simplify [5+(3)]. This is a straightforward addition: 5 plus 3 equals 8. Easy peasy! Now, let's move on to the second set of parentheses: (6-7). This is 6 minus 7, which gives us -1. Think of it as starting at 6 and moving 7 spaces to the left on the number line. We end up at -1. So, after simplifying both sets of parentheses, our equation is now super streamlined: 8 + (-1). Can you believe how much we've simplified this from the original problem? This step demonstrates the power of breaking down a complex problem into smaller, more manageable parts. By systematically addressing each element, we've made the equation much less daunting. Simplifying parentheses is a crucial step in the order of operations, and we've nailed it! Now, we're down to just a simple addition problem. We're almost there, guys! Just one more step to go, and we'll have the final answer. Let's keep up the momentum and finish strong!

Step 4: The Final Calculation

We're in the home stretch now! Our equation has been beautifully simplified to: 8 + (-1). This is the final calculation, and it's a piece of cake. Adding a negative number is the same as subtracting the positive version of that number. So, 8 + (-1) is the same as 8 - 1. And what's 8 minus 1? You guessed it: 7! So, the final answer to our problem [-(4-9)+(-5+8)]+(6-7) is 7. Give yourselves a huge pat on the back! You've successfully navigated through the order of operations and solved a problem that might have seemed tricky at first. This final step brings together all the previous simplifications to arrive at the solution. It highlights the importance of each step in the process – without simplifying the parentheses and handling the negative signs, we wouldn't have been able to reach this point. This is a fantastic example of how breaking down a complex problem into smaller, manageable steps can lead to a clear and accurate solution. You've demonstrated your understanding of the order of operations and your ability to apply it effectively. Congratulations on solving this problem! You've earned it!

Conclusion: You Did It!

Fantastic job, everyone! We've successfully solved the equation [-(4-9)+(-5+8)]+(6-7), and the answer is 7. You've not only learned how to solve this specific problem, but you've also reinforced your understanding of the order of operations (PEMDAS/BODMAS), which is a fundamental skill in mathematics. Remember, math isn't about memorizing formulas, it's about understanding the process and applying the rules logically. By breaking down the problem into smaller steps – simplifying parentheses, dealing with negative signs, and performing the final calculation – we made a seemingly complex equation much more manageable. This approach is key to tackling any mathematical challenge. So, the next time you encounter a problem that looks intimidating, remember the steps we took today: breathe, break it down, and conquer it! You have the tools and the knowledge to succeed. Keep practicing, keep learning, and most importantly, keep believing in yourself. You've proven that you can handle these types of problems, and with continued effort, you'll become even more confident and proficient in math. Congratulations again on your success! You've rocked it!