Solving Math Expressions: A Step-by-Step Guide

Hey guys! Let's dive into this math problem. We're going to break it down step-by-step so it's super easy to understand. The core of this problem revolves around evaluating an expression: (-15.2) + x + (-3.1), with the added info that x = 7. Our mission? Find the value of this expression. Sounds fun, right?

First things first, what does the problem actually ask us to do? Essentially, we are presented with an algebraic expression. To solve the question, we need to carefully incorporate the value of 'x' which is conveniently given to us. This means that we are going to substitute every instance of 'x' in the provided expression with the numerical value provided. After substituting the variables, we will simplify the expression to determine the numerical result. Remember, the goal is to carefully perform the calculations and arrive at the right answer!

Let's get started. We have the expression (-15.2) + x + (-3.1). We are also told that x = 7. So, let's substitute 'x' with '7' in the expression. This will turn the equation into (-15.2) + 7 + (-3.1). Now, we just have to compute this equation to find the value of our expression. We can approach this in different ways. For example, we can add all the negative numbers together. That is, we can add -15.2 and -3.1, and then finally add 7. We can also simply add the first 2 numbers and then the result can be added by the third number. No matter which method is chosen, the final outcome must be the same.

Now, let's start with the left of the expression. -15.2 + 7. When we add these numbers, we have to subtract the smaller number from the larger number (ignoring the negative sign for a second) which is 15.2-7 which equals to 8.2. Since the larger number had a negative sign, we assign a negative sign to the answer, resulting in -8.2. Now, add -3.1 to -8.2, which is essentially -8.2-3.1 which equals to -11.3. So, the total of the expression is -11.3.

Okay, let's break this down further, just to make absolutely sure we've got it. We are looking for the value of (-15.2) + 7 + (-3.1). When dealing with mixed positive and negative numbers, it's often helpful to group the negatives together. So, let's rewrite the expression a bit. Imagine we're collecting all the 'debt' (the negative numbers) and all the 'assets' (the positive numbers). We have -15.2 and -3.1 as debts, and +7 as an asset. First, combine the debts: -15.2 + (-3.1) = -18.3. This means we have a total debt of 18.3. Then, we can add our asset: -18.3 + 7. Now we have a debt of 18.3, but we're paying off 7 of it. So, 18.3 - 7 = 11.3. But since we still owe more than we have, the answer is negative: -11.3. So the value of the equation is -11.3

Decoding the Answer Choices

Alright, now that we've found our answer to be -11.3, we're not done yet. We need to check the answer choices provided in the original question. If you look at the choices, none of them match our result, -11.3. This indicates that there might be an error in the original problem or the answer choices given. However, the process we followed is correct. Now, if you are asked to select an answer among the existing choices, we would need to check which one of the answer choices is the closest to the answer to the provided expression. If we were to pick the closest, we would pick the answer closest to -11.3, which would be either -1.7, -81.7, 18.3, or -31. Each of these values are very far from -11.3 and could suggest a misprint of the original problem or answers. If we are asked to find the range that the answer could lie in, we could suggest that based on the provided answers, we can't find an answer to this expression.

Keep in mind that when you encounter a math problem, the most important thing is to understand the concepts and the steps involved. Even if the given answer choices are incorrect, you can still confidently arrive at the correct solution using the right approach. Practice consistently, and you'll become a pro at solving these types of problems!

Understanding the Basics: Order of Operations

Before we wrap things up, let's quickly chat about the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)). This is the secret sauce for solving any mathematical expression, ensuring everyone gets the same correct answer. The order is extremely important, guys. Get it wrong, and you'll end up in a world of confusion!

So, what does PEMDAS mean in practice? First, you tackle anything inside parentheses. Then you address any exponents (powers and roots). Next comes multiplication and division, working from left to right. Lastly, you handle addition and subtraction, also from left to right. Now, in our specific problem, we don't have exponents, and we deal with only addition and subtraction. But knowing the rules, in general, is crucial for everything.

Understanding the order of operations helps you break down complex expressions into manageable chunks. It provides a roadmap, guiding you through the problem step by step. When you follow the correct order, you can confidently solve any math equation and avoid common mistakes. Think of PEMDAS as your best friend, always there to give you the correct route. By mastering PEMDAS, you build a strong foundation for tackling more complicated mathematical concepts in the future!

Practicing Makes Perfect

So, we've walked through solving the expression step by step, reviewed the answer choices, and talked about order of operations. What's next? The secret to mastering math is practice. The more you work through problems, the more comfortable and confident you'll become. Grab some practice problems. Mix and match those positive and negative numbers. Use the PEMDAS as your guide, and don't be afraid to make mistakes. Mistakes are your best teachers! Take those mistakes as an opportunity to learn and improve. Identify where you went wrong, review the concepts, and try again. Each time you solve a problem, you get stronger and build a solid foundation.

Find a good source of practice problems. If your textbook has examples, use those, or search online for practice worksheets or interactive tutorials. Many websites and apps offer a wealth of problems to hone your skills. Remember, practice shouldn't feel like a chore. Make it a game. Turn on some music, find a comfortable spot, and challenge yourself. Set small goals and reward yourself when you reach them. The journey of math can be fun and rewarding, and your effort will eventually pay off! With consistent effort and a positive attitude, you'll be amazed at how far you can go.

Wrapping it Up

Alright, that's a wrap, guys! We have successfully tackled the math expression, examined answer choices, and dived into the importance of order of operations and practice. Remember, math is like any other skill. It takes time, effort, and the right approach. Break the problems into smaller steps, review the fundamental concepts, and practice consistently. Don't be afraid to seek help if you need it. There are plenty of resources available to guide you along the way. Stay curious, keep learning, and celebrate your progress. Every problem you solve, every concept you understand, brings you closer to mastering math. So, keep up the great work, and never stop exploring the fascinating world of numbers and equations! Keep practicing and you will do great!