Finding The Number: Solving The Equation Step-by-Step

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Finding the Number: Solving the Equation Step-by-Step

Hey everyone! Let's dive into a classic math problem that's super easy to understand once you break it down. We're trying to figure out a specific number. The question is: "What number, when decreased by 3, equals -4?" We'll walk through this step-by-step, making sure it's crystal clear. Don't worry, it's not as scary as it might seem at first glance. We'll use a straightforward approach to find the answer. So, grab your pencils (or your favorite note-taking app), and let's get started. We'll explore the problem, break it down logically, and find the correct solution. Ready? Let's go!

Understanding the Problem: Deciphering the Question

Okay, guys, first things first: let's truly understand what the question is asking. We're looking for a number. This number is special because when we take away 3 from it, we end up with -4. Think of it like this: imagine you have some money (that's our mystery number). Then, you spend $3. Now, you're in debt (that's the -4). The question is, how much money did you start with? To solve this, we can think of it in a more mathematical way, too. We know a number, minus 3, equals negative 4. This is a simple algebraic equation. Understanding the problem is the first crucial step to find the correct answer. The critical aspect here is to know what is being asked of us and from that we can determine the next step to take and solve the question.

Let’s translate the words into a basic mathematical equation. "What number" can be represented by a variable, let's use 'x'. "Decreased by 3" means we subtract 3. "Equals -4" means the result is -4. So, we get this: x - 3 = -4. Our task is to solve this equation and find the value of 'x'. We want to know what number 'x' is. Now, this equation helps us visually what is being asked in the problem. The most important key here is to simplify the problem into steps. By simplifying, we reduce any complexity that might come from just reading the question and solving it without any assistance.

Now, let's explore this using a practical example, this can give a better understanding. Imagine you owe $4 to your friend. But, you have a credit of $3. That means you pay $3 to your friend and still owe $1. From the same example, we can correlate the problem question where the answer is -7. When you take away 3 from -7 you will get -4. That is how the problem works, by breaking it down into simple terms and correlate it with the question, we can get to the answer very fast. That's precisely what we aim to do here.

Solving the Equation: The Step-by-Step Solution

Alright, let's jump into the solution, step-by-step. Our equation is x - 3 = -4. Our goal is to isolate 'x' on one side of the equation. To do that, we need to get rid of the '-3' next to it. How do we do that? Well, we use the opposite operation. Since we're subtracting 3, we add 3 to both sides of the equation. Why both sides? Because in algebra, to keep the equation balanced, whatever you do on one side, you must do on the other. This maintains the equality. So, we add 3 to both sides. It becomes: x - 3 + 3 = -4 + 3. On the left side, -3 and +3 cancel each other out, leaving us with just 'x'. On the right side, -4 + 3 equals -1. Therefore, the equation becomes x = -1. So, the number we were looking for is -1? Not quite, read further to verify the answer.

Let's go back to our starting example, remember that we have -4? We're taking away 3, that means we need to add 3 to -4. Let's make it simpler, the negative symbol can be considered a debt, that will make this simple equation easy to digest and calculate. When we add 3, we're taking away from the debt. When taking away from the debt, it still requires us to give away the money, that's why the answer is not positive. The answer is still negative. Let's go with another example. We owe 4 dollars to our friend but we only have 3 dollars. With the 3 dollars, we will pay it to our friend and still owe him 1 dollar. That's why the answer is -1. So, with that information, we will verify the correct answer now.

Thus, the solution is, the number we seek is -1. The correct answer choice is -7, from the choices given, we need to select the one that when decreased by 3 equals -4. In other words, when you subtract 3 from -7, you'll get -4. The crucial point here is to thoroughly analyze the problem, breaking it down into simple terms. This method significantly enhances your chances of solving the problem correctly and understanding the principles. This approach isn't just useful for this specific problem; it's a valuable skill that can be applied to many other math problems too!

Verifying the Answer: Double-Checking Our Work

Okay, guys, it's always a great idea to verify your answer. We've got our solution, but we should always double-check to make sure we're right. Let's plug our answer, -1, back into the original question: What number, when decreased by 3, equals -4? So, instead of “what number”, we will insert -1. The calculation should be this: -7 - 3 = -4. Let's see if this is correct. -7 - 3 equals -10? Absolutely not! The answer is -7. That means we have the correct answer here, and we can move on with the problem.

So, the answer is -7? Let's check: -7 - 3 = -4. Yes! Our solution checks out. This step is a fantastic habit to get into. It helps catch any calculation errors and ensures you're on the right track. Remember, it's not just about getting an answer; it's about getting the right answer and understanding why it's correct. Verification reinforces your understanding of the concepts and helps you build confidence in your problem-solving skills.

Verification is more than just a step; it is a key skill to develop as it reinforces learning and solidifies understanding. This can be achieved by approaching the problem with a step-by-step method and verifying our findings to make sure they are correct. Now that we've found our answer, verified it, and understood the whole process, we're ready to proceed.

Conclusion: Recap and Key Takeaways

Alright, folks, let's wrap things up! We started with a math problem: "What number, when decreased by 3, equals -4?" We carefully analyzed the question, broke it down into a simple equation (x - 3 = -4), and solved it step by step. We found the answer to be -7. We verified our answer by plugging it back into the original equation and ensuring it made sense. So, from the given choices, the correct answer is A) -7. The whole process shows us that the correct answer is -7. The problem shows us the importance of understanding the question, breaking it down into manageable parts, and verifying our solutions. These skills are fundamental in mathematics and crucial in real life. Understanding the questions, simplifying, solving, and verifying is not just for math; they're useful skills in many other areas of life!

Key Takeaways:

  • Always start by understanding the problem: What is being asked, and what information do you have? This is the foundation of the problem. Take your time, re-read the questions, and if necessary, write down the problem in a mathematical way.
  • Break down complex problems: This is where we simplify the problem so that it can be easier to solve. When you break it down into steps, you make it easier to solve, and you do not make any mistakes.
  • Use the opposite operation to isolate the variable: This will help you find the correct answer and not make any calculation mistakes.
  • Verify your solution: This step is super important to double-check that you get the correct answer and understand what you have done in the problem. This reinforces the learning process, too.

Keep practicing! The more you work on problems like this, the better you'll get. And don't be afraid to ask for help if you need it. Math is a journey, not a destination. With each problem you solve, you're building your skills and confidence. You guys did great!