Solve 125x = 600: Step-by-Step Solution

Hey guys! Let's dive into this math problem together. We've got a straightforward equation: 125 multiplied by x equals 600. Our mission? To figure out what x is. Don't worry, it's easier than it looks! We will break this down and solve it step by step.

Understanding the Problem

So, the main question we're tackling is: "What number, when multiplied by 125, gives us 600?" That's the essence of what we need to solve. In mathematical terms, we're dealing with a simple algebraic equation. Algebraic equations, at their core, are about finding unknown values. These unknowns are often represented by letters – in our case, it’s x. The equation is like a balanced scale; both sides must remain equal. Our goal is to isolate x on one side to reveal its value. Think of it as peeling back layers to reveal the hidden number. We'll use basic arithmetic operations to maintain this balance while simplifying the equation. This approach isn't just about getting the right answer; it's about understanding the underlying principles of algebra. It’s like learning the rules of a game, which then allows you to play any variation of it. So, let's get started and unravel this mathematical puzzle together! This method of solving equations is a fundamental skill in mathematics and will be super useful as you tackle more complex problems. Remember, every equation is just a puzzle waiting to be solved!

The Basic Strategy: Isolating x

The secret to cracking this equation is isolating our mystery variable, x, on one side of the equals sign. Think of it like this: we want to get x all by itself so it can tell us its value. The equation we're starting with is 125 × (x) = 600. Currently, x is being multiplied by 125. To undo this multiplication and free x, we need to perform the inverse operation. What's the opposite of multiplication? Division, you guessed it! We're going to divide both sides of the equation by 125. Remember that golden rule of equations: what you do to one side, you must do to the other. This keeps the equation balanced, like a perfectly level seesaw. This principle is crucial in algebra, ensuring that the equality remains valid throughout the solving process. By dividing both sides by 125, we maintain this balance while making progress toward our goal. It's like a carefully choreographed dance, where each step ensures harmony and equilibrium. So, let’s perform this step and watch how the equation transforms, bringing us closer to the solution. It's like watching a puzzle piece slide perfectly into place.

Step-by-Step Solution

Okay, let's get our hands dirty and solve this thing! Remember, our equation is 125 × (x) = 600. To isolate x, we're going to divide both sides by 125. Here’s how it looks:

(125 × x) / 125 = 600 / 125

On the left side, 125 divided by 125 is simply 1. So, we're left with:

x = 600 / 125

Now, we need to do the division. 600 divided by 125. You can use a calculator, do long division, or try to simplify the fraction first. Let's simplify! Both 600 and 125 are divisible by 25. So, we can simplify the fraction:

600 / 25 = 24

125 / 25 = 5

So, our fraction becomes:

x = 24 / 5

Now, we divide 24 by 5, and we get:

x = 4.8

Ta-da! We've solved for x. The value of x that makes the equation true is 4.8. It's like finding the missing piece of a jigsaw puzzle. Each step we took was deliberate, and each operation brought us closer to the solution. Remember, in math, as in life, breaking things down into smaller steps makes the journey much easier. Now that we've found our answer, let's double-check it to make sure it fits perfectly.

Checking Our Answer

Alright, before we do a victory dance, let's make absolutely sure our answer is correct. This is a crucial step in problem-solving – always double-check! We found that x = 4.8. To check, we'll plug this value back into our original equation:

125 × x = 600

Substitute x with 4.8:

125 × 4.8 = 600

Now, let's do the multiplication. If you multiply 125 by 4.8, you'll indeed get 600. That's awesome news! This confirms that our solution is correct. Checking your work is like putting on a seatbelt – it's an extra layer of safety. It ensures that you're not just getting an answer, but the right answer. This practice not only validates your solution but also reinforces your understanding of the problem-solving process. It’s a habit that will serve you well in mathematics and beyond. So, always take that extra minute to check; it’s totally worth it. Now that we've verified our result, we can confidently say we've nailed it!

The Final Answer

Drumroll, please! After all our calculations and checks, we've arrived at our final answer. The value of x in the equation 125 × (x) = 600 is:

x = 4.8

There you have it! We've successfully solved the equation. It's like reaching the summit of a mountain after a good climb. Each step, each calculation, brought us closer to the peak. We started with a problem, broke it down, solved it step by step, and then double-checked our answer. This process is not just about getting the right number; it's about building confidence in your problem-solving abilities. Remember, every math problem is a challenge, an opportunity to flex your brain muscles. And with each problem you solve, you become a stronger, more confident mathematician. So, let's celebrate this victory and get ready for the next challenge. Because in the world of math, there's always something new and exciting to discover. Keep exploring, keep questioning, and most importantly, keep having fun with math!