Unlocking The Equation: Step-by-Step Guide To Solve For X

Hey Plastik Magazine readers! Let's dive into a classic algebra problem. We're going to tackle the equation 6x - 9 = -75 and figure out the value of x. Don't worry, it's not as scary as it looks. We'll break it down into simple, easy-to-follow steps. Think of it like a puzzle – we're just rearranging the pieces to find the missing value. This kind of problem is fundamental in mathematics, so understanding it will help you in many different areas. You can use this knowledge in more complex equations, geometry, or even in real-life scenarios that involve calculations.

Before we start, let's go over the basics of what we're doing. Our main goal is to isolate x on one side of the equation. This means we want to get x all by itself, with a number on the other side. To do this, we'll use a few simple rules, like adding or subtracting the same number from both sides of the equation and multiplying or dividing both sides by the same number. Remember, what you do to one side, you must do to the other side to keep the equation balanced. This is crucial; otherwise, you change the whole equation. The good thing about equations is that they are like a balanced scale. If you add or remove weight from one side, the scale tips. To keep it balanced, you do the exact same thing to the other side. So, in our case, we will add or subtract numbers to keep the balance until we get x alone on one side. This process will help you practice and build your confidence in your math skills, which is the key to solving equations like these. Now, let's get down to business! Ready?

Step-by-Step Solution

Step 1: Isolate the Term with x

Our first step in solving the equation 6x - 9 = -75 is to get the term with x (which is 6x) by itself on one side of the equation. Right now, we have -9 hanging out with it, and we need to get rid of that. To do this, we'll use the addition property of equality. This means we'll add the same number to both sides of the equation. Since we have -9, we'll add 9 to both sides. Why 9? Because -9 + 9 = 0, and that will eliminate the -9 on the left side, leaving us with only the 6x term. So, let’s do it:

6x - 9 + 9 = -75 + 9

On the left side, -9 + 9 cancels each other out, leaving us with 6x. On the right side, -75 + 9 = -66. So now our equation looks like this:

6x = -66

See? We're already making progress. This step is all about simplifying the equation, making it easier to solve. Think of it as peeling off layers of an onion – we're gradually getting closer to the core, which is the value of x. Always remember that any operation you do to one side of the equation, you must do to the other side. This principle is fundamental to the concept of the equation; otherwise, you'll change the problem.

Step 2: Solve for x

Now that we've isolated the term with x ( 6x = -66), we need to get x all by itself. Right now, x is being multiplied by 6. To undo this, we'll use the division property of equality. This means we'll divide both sides of the equation by the same number, which in this case is 6. Why 6? Because 6 divided by 6 equals 1, and 1* x is just x. So, let's divide both sides by 6:

(6x) / 6 = -66 / 6

On the left side, 6 / 6 cancels out, leaving us with just x. On the right side, -66 / 6 = -11. So now our equation looks like this:

x = -11

And there you have it, guys! We have successfully solved for x. The value of x is -11. This step is usually the last and simplest one. After doing this, you'll find the value of x very quickly. Remember to double-check your work to ensure everything is correct. It's always a good practice to go back and check your work to make sure everything is perfect and the solution is correct.

Step 3: Check Your Answer

It's always a great idea to check your answer to make sure you didn't make any mistakes along the way. To do this, substitute the value of x (-11) back into the original equation and see if it holds true. Remember the original equation? It was 6x - 9 = -75. Let's plug in -11 for x:

6 * (-11) - 9 = -75

First, multiply 6 by -11: 6 * -11 = -66. Now the equation looks like this:

-66 - 9 = -75

Then subtract 9 from -66: -66 - 9 = -75

-75 = -75

Since -75 does indeed equal -75, our answer is correct! This step is essential because it gives us a clear confirmation that our calculations were on point. This is an excellent way to practice and build your confidence in your math skills. Double-checking your work also reinforces the concepts and helps you understand the problem better. Always do this step after you've found the result to confirm that the calculations are correct.

Conclusion: The Answer

So, after all that work, the answer is B. -11. We started with the equation 6x - 9 = -75, and by following these simple steps, we found that x equals -11. Solving these types of equations is a fundamental skill in algebra and is a cornerstone for more complex math problems. Remember to always isolate x, then solve for x, and finally, check your answer. Keep practicing, and you'll become a pro at these problems in no time. Congratulations, guys, you did it! Now you know how to solve for x in a simple linear equation. Keep practicing, and you'll become a pro at these problems in no time.