Solving Equations: Step-by-Step Guide
Hey everyone! Today, we're diving into the world of equations. Specifically, we're going to solve the equation $-1.3 = x - (-13.2)$. Don't worry if it looks a little intimidating at first; we'll break it down step by step to make sure you understand everything. This is a fundamental concept in mathematics, and understanding how to solve equations is super important for all sorts of problem-solving. So, let's get started!
Understanding the Basics of Equations
Alright, before we jump into the problem, let's make sure we're all on the same page about what an equation is. An equation is simply a mathematical statement that shows that two expressions are equal. Think of it like a balanced scale. On each side of the equals sign (=), we have an expression, and the equation tells us that these two expressions have the same value. Our goal when solving an equation is to find the value of the unknown variable, which in our case is 'x'. This is like figuring out the weight of an object to balance the scale. To do this, we use various properties of equality to manipulate the equation until the variable is isolated on one side, and the solution is revealed on the other. It's like a mathematical puzzle; each step brings us closer to the answer. The properties of equality are our tools here. For example, the addition property of equality states that if we add the same number to both sides of an equation, the equation remains true. This is key because it allows us to 'undo' operations and gradually simplify the equation. Similarly, the subtraction property of equality tells us that subtracting the same number from both sides maintains the balance. Multiplication and division properties also play vital roles, allowing us to solve more complex equations. Understanding these properties and how to apply them is the foundation for solving more complicated equations later on. So, as we go through this, keep in mind how these properties are being used to maintain the equation's balance. Each step we take is about preserving that balance while isolating the variable we're trying to solve for. It's all about logical manipulation to unveil the solution.
Now, let's move on and solve the equation itself. Ready? Let's do this!
Step-by-Step Solution
Okay, so we've got the equation $-1.3 = x - (-13.2)$. Our main goal is to find the value of 'x'. To get 'x' by itself, we need to get rid of the stuff around it. Here’s how we'll do it, step by step:
Step 1: Simplify the Equation
First things first, let's simplify the equation a bit. Notice the double negative in front of 13.2? Remember, minus a negative is the same as plus. So, we can rewrite the equation as:
See how much cleaner that looks? This initial simplification makes the next steps a lot easier to handle. Always be on the lookout for ways to simplify the initial setup; it reduces the chances of making mistakes down the line. It's like tidying up your workspace before starting a big project. It helps to keep everything organized and ensures you're less likely to run into unexpected problems. Take this opportunity to double-check that you've correctly applied all the rules of operations, especially when dealing with negative signs. Accuracy in this step is crucial because it forms the foundation for all the steps that follow. So, take your time, make sure your simplification is spot-on, and you'll be well on your way to getting the correct answer. The key is to start by addressing the immediate operations present, in this case, the double negative, and transforming them into a more manageable form. That simplifies the process to follow.
Step 2: Isolate the Variable
Now, we want to get 'x' all alone on one side of the equation. To do this, we need to get rid of the +13.2. We can do this by using the subtraction property of equality. We're going to subtract 13.2 from both sides of the equation. This maintains the balance.
Step 3: Perform the Calculation
Now, let's do the math on both sides.
On the left side: $-1.3 - 13.2 = -14.5$
On the right side: $x + 13.2 - 13.2 = x$
So, our equation now looks like this:
Step 4: State the Solution
And there you have it! We've isolated 'x', and we know its value. The solution to the equation $-1.3 = x - (-13.2)$ is:
Verification of the Solution
It's always a good idea to check your answer. Plug the value of 'x' back into the original equation to see if it works. So, let’s substitute -14.5 for 'x' in the original equation: $-1.3 = x - (-13.2)$. This becomes $-1.3 = -14.5 - (-13.2)$. Remember that subtracting a negative is the same as adding, so we rewrite it as $-1.3 = -14.5 + 13.2$. If we perform the calculation on the right side of the equation, we get -1.3, which is exactly what’s on the left side! This confirms that our solution is correct. Checking the solution provides a useful review of the problem and the steps. This step makes sure you haven't made any mistakes during the solving process. Verification builds confidence in your final answer and also strengthens your understanding of the underlying principles. In the beginning, this is a great habit to adopt, especially when you are just learning how to solve equations. As you grow more familiar with this type of math, it gets easier and less likely to have errors, but checking your work is always smart.
Conclusion
And that's a wrap, guys! We successfully solved the equation $-1.3 = x - (-13.2)$. We did it by simplifying the equation, isolating the variable, performing the calculations, and verifying our answer. Solving equations is a super important skill in mathematics, and with practice, you'll become a pro at it! Keep practicing, and don't be afraid to try different problems. The more you work with equations, the easier they will become. Remember, every equation you solve builds your confidence and understanding of math concepts. So keep going, and you'll do great! And that's all, folks!
