Solving For X: -4.5(x-8.9) = 12.6 - A Step-by-Step Guide

Hey Plastik Magazine readers! Ever get stuck on an equation and feel like you're staring at a jumble of numbers and symbols? Don't worry, we've all been there! Today, we're going to break down how to solve the equation -4.5(x - 8.9) = 12.6 step-by-step. Think of it as a fun puzzle – we're just trying to find the missing piece, which in this case, is the value of x. So, grab your pencils and let's dive in! This guide is designed to be super clear and easy to follow, so even if math isn't your favorite subject, you'll be able to tackle this problem with confidence. We'll cover each step in detail, explaining the logic behind it and making sure you understand why we're doing what we're doing. After all, understanding the why is just as important as knowing the how.

Step 1: Distribute the -4.5

The first thing we need to do is get rid of those parentheses. Remember the distributive property? It basically means we need to multiply the -4.5 by everything inside the parentheses. This is a crucial step because it simplifies the equation and makes it easier to work with. It's like untangling a knot before you try to tie it tighter – makes the whole process smoother! When we distribute, we get: -4.5 * x + (-4.5 * -8.9) = 12.6. Notice how we're careful with the signs here. A negative times a negative becomes a positive, which is super important for getting the correct answer. Now, let's simplify this a bit further. Multiplying -4.5 by x gives us -4.5x. And multiplying -4.5 by -8.9 gives us a positive number. To be precise, -4.5 multiplied by -8.9 equals 40.05. So, our equation now looks like this: -4.5x + 40.05 = 12.6. See? We've already made progress and the equation is looking less intimidating. This step is all about clearing the way and setting us up for the next move. Think of it as organizing your workspace before you start a project – a little prep goes a long way!

Step 2: Isolate the Term with x

Now that we've distributed and simplified, our next goal is to isolate the term with x on one side of the equation. This means we want to get the -4.5x by itself. To do this, we need to get rid of the +40.05 that's hanging out on the same side. The way we do that is by using the opposite operation. Since we're adding 40.05, we need to subtract 40.05 from both sides of the equation. This is a fundamental rule in algebra: whatever you do to one side, you must do to the other to keep the equation balanced. It's like a seesaw – if you take weight off one side, you need to take the same weight off the other to keep it level. So, we subtract 40.05 from both sides: -4.5x + 40.05 - 40.05 = 12.6 - 40.05. On the left side, the +40.05 and -40.05 cancel each other out, leaving us with just -4.5x. On the right side, 12.6 minus 40.05 is -27.45. Therefore, our equation now reads: -4.5x = -27.45. We're getting closer! We've successfully isolated the term with x, and now we're just one step away from finding the value of x itself. This part is all about strategic maneuvering, moving things around to get what we want.

Step 3: Solve for x

Alright, we're in the home stretch! We've got -4.5x = -27.45, and now we need to solve for x. This means we need to get x all by itself. Right now, x is being multiplied by -4.5. To undo that multiplication, we need to do the opposite operation: division. So, we're going to divide both sides of the equation by -4.5. Again, remember the golden rule: whatever you do to one side, you gotta do to the other. It's all about maintaining balance and fairness in the equation. Let's divide: (-4.5x) / -4.5 = (-27.45) / -4.5. On the left side, -4.5 divided by -4.5 is just 1, so we're left with 1*x, which is simply x. On the right side, -27.45 divided by -4.5 is a positive number (a negative divided by a negative is positive). If you plug that into a calculator (or do it by hand, if you're feeling ambitious!), you'll find that -27.45 divided by -4.5 equals 6.1. So, drumroll please... we have our answer! x = 6.1. We did it! We solved the equation and found the value of x. This final step is the culmination of all our hard work, the moment where everything clicks into place.

Conclusion

So, there you have it! We've successfully solved the equation -4.5(x - 8.9) = 12.6 and found that x = 6.1. Not so scary after all, right? Remember, the key to solving algebraic equations is to break them down into smaller, manageable steps. Distribute, isolate, and then solve. And always, always remember to do the same thing to both sides of the equation. It's like a mathematical dance – you need to keep the steps balanced and coordinated. We hope this step-by-step guide has been helpful and that you feel more confident tackling similar problems in the future. Math might seem intimidating sometimes, but with a little patience and the right approach, you can conquer any equation. Keep practicing, keep exploring, and most importantly, keep having fun with math! Until next time, Plastik Magazine readers!