Solving Equations: 2x + 3 = 5 - 6 Explained
Hey everyone! Ever stumbled upon an equation like 2x + 3 = 5 - 6 and felt a little lost? Don't worry, you're definitely not alone! Solving equations might seem tricky at first, but trust me, with a little guidance, it becomes super manageable. In this article, we're going to break down exactly how to solve this specific equation step-by-step. We'll go through each stage, making sure you grasp every concept. Our aim is to make this process crystal clear. Letâs begin our journey of demystifying mathematical equations and turning you into an equation-solving pro! This is more than just a tutorial; think of it as your personal guide to understanding and conquering algebra. By the end, you'll have the confidence to tackle similar problems with ease. We'll also touch on why understanding these basics is so vital for more complex math and real-world applications. So, buckle up, grab a pen and paper, and let's dive in to make solving equations a breeze. We'll ensure that even the most complex equation is broken down, so that anyone can understand it. We are going to make you a math pro, so that you can show off to your friends. Let's go ahead and do it. Ready to simplify the equation 2x + 3 = 5 - 6?
Understanding the Basics: What is an Equation?
Okay, before we jump into the nitty-gritty, letâs make sure we're all on the same page. What exactly is an equation? Well, in simple terms, an equation is a mathematical statement that shows two expressions are equal. Think of it like a balanced scale. On one side, you have one expression, and on the other side, you have another. The equal sign (=) is the fulcrum that keeps everything in balance. Equations often include variables, which are usually represented by letters like 'x', 'y', or 'z'. These variables stand for unknown values that we need to find. The goal of solving an equation is to find the value of the variable that makes the equation true. For example, in the equation x + 2 = 5, the variable 'x' has a value of 3 because 3 + 2 does indeed equal 5. The basic principle of solving equations involves isolating the variable on one side of the equation. This means getting the variable by itself. To do this, we use inverse operations, which are operations that undo each other. Addition and subtraction are inverse operations, as are multiplication and division. When we perform an operation on one side of the equation, we must perform the same operation on the other side to maintain the balance. Think of it like adding or removing weights from both sides of the scale â it keeps everything balanced. So, remember: equations are all about balance, and keeping that balance is key to solving them correctly. We're going to walk through each of these concepts so that you'll know how to solve these kinds of math problems. It's going to be a fun and very educational ride.
Step-by-Step Solution: Breaking Down 2x + 3 = 5 - 6
Alright, time to roll up our sleeves and get to work! We're going to tackle the equation 2x + 3 = 5 - 6 step-by-step, so you won't miss a thing. First, we must simplify both sides of the equation to make the numbers as simple as possible. Remember our goal: to isolate 'x' and find its value. Let's begin! The equation is 2x + 3 = 5 - 6.
- Step 1: Simplify the Right Side: The right side of the equation is
5 - 6. This simplifies to-1. So, our equation now looks like this:2x + 3 = -1. We have successfully streamlined the equation's right side. - Step 2: Isolate the Term with 'x': Now, we want to get the term with 'x' (which is
2x) by itself. To do this, we need to get rid of the+ 3on the left side. We do this by subtracting 3 from both sides of the equation. Remember, whatever we do to one side, we have to do to the other. Therefore:2x + 3 - 3 = -1 - 3. This simplifies to2x = -4. By subtracting 3 from both sides, we've moved closer to isolating 'x'. - Step 3: Solve for 'x': The last step is to solve for 'x'. We have
2x = -4. To isolate 'x', we need to divide both sides of the equation by 2:2x / 2 = -4 / 2. This simplifies tox = -2. We've found our solution! 'x' equals -2. This means if we substitute -2 for 'x' in the original equation, it should be true. Now, you've solved the equation, great job!
Verifying Your Solution: Checking Your Answer
Awesome! We've solved the equation and found that x = -2. But how do we know if we're right? The best way to be sure is to verify the solution. This involves substituting the value of 'x' back into the original equation and checking if both sides are equal. It's like a self-check to ensure everything is correct. Let's do it with our equation, 2x + 3 = 5 - 6. We'll substitute -2 for 'x': 2(-2) + 3 = 5 - 6. Simplify the left side: 2 * -2 = -4, so we have -4 + 3. This equals -1. Simplify the right side: 5 - 6 = -1. So, the equation becomes -1 = -1. Because both sides are equal, our solution, x = -2, is correct! Verification is a crucial step in solving equations because it helps catch any mistakes we might have made along the way. It's a way of ensuring that your answer is accurate and gives you extra confidence in your abilities. Always make sure to double-check your work. It's a fundamental part of problem-solving in math.
Why Understanding this Matters: Real-World Applications
Why does all this matter? You might be wondering,
