Solving For X In The Equation -1.5 + X/6 = -20.7 A Step-by-Step Guide

Introduction

Hey guys! Today, we're diving into a simple yet crucial algebraic problem: solving for x in the equation -1.5 + x/6 = -20.7. This type of problem is fundamental in mathematics and appears frequently in various real-world applications. Understanding how to isolate a variable and solve for its value is a key skill. We'll break down the steps in a super clear and friendly way, so whether you're a student tackling homework or just brushing up on your algebra, you'll find this guide helpful. We’ll go through each step meticulously, ensuring that you not only get the answer but also grasp the underlying concepts. By the end of this article, you’ll be able to confidently solve similar equations and understand the logic behind each operation. So, let’s jump right in and demystify the process of solving for x! This skill is essential for more advanced mathematical concepts, and mastering it now will set you up for success in future studies and problem-solving scenarios. Remember, math isn't just about finding the right answer; it’s about understanding how to find it. Let's get started and make sure you're equipped with the knowledge and confidence to tackle any algebraic equation that comes your way.

Step-by-Step Solution

Step 1: Isolate the Term with x

The primary goal in solving for x is to isolate the term that contains x, which in our equation is x/6. To do this, we need to get rid of the -1.5 on the left side of the equation. How do we do that? We use the principle of inverse operations. The inverse operation of subtraction is addition. So, we add 1.5 to both sides of the equation. This keeps the equation balanced, which is super important in algebra. Think of it like a scale: if you add something to one side, you have to add the same thing to the other side to keep it balanced. Adding 1.5 to both sides looks like this:

-1.5 + x/6 + 1.5 = -20.7 + 1.5

When we simplify this, the -1.5 and +1.5 on the left side cancel each other out, leaving us with:

x/6 = -20.7 + 1.5

Now, we need to perform the addition on the right side. Adding 1.5 to -20.7 gives us -19.2. So, the equation now looks like this:

x/6 = -19.2

We've successfully isolated the term with x! This is a big step because we're one step closer to finding the value of x. Remember, the key here is to use inverse operations to move terms around the equation. By adding 1.5 to both sides, we maintained the equation's balance and simplified it, bringing us closer to our solution. Now, let's move on to the next step and figure out how to get x all by itself.

Step 2: Solve for x

Now that we have the equation x/6 = -19.2, the next step is to isolate x completely. Currently, x is being divided by 6. To undo this division, we need to perform the inverse operation, which is multiplication. We'll multiply both sides of the equation by 6. Again, it's super important to do the same operation on both sides to maintain the balance of the equation. If we only multiplied one side, the equation wouldn't hold true anymore. So, multiplying both sides by 6 looks like this:

(x/6) * 6 = -19.2 * 6

On the left side, the multiplication by 6 cancels out the division by 6, leaving us with just x. On the right side, we need to multiply -19.2 by 6. This gives us -115.2. So, the equation simplifies to:

x = -115.2

And there you have it! We've solved for x. The value of x that satisfies the original equation -1.5 + x/6 = -20.7 is -115.2. This step demonstrates the power of using inverse operations to isolate the variable you're trying to solve for. By multiplying both sides by 6, we effectively undid the division and found the value of x. Remember, the key to solving these types of equations is to carefully apply inverse operations while ensuring you keep the equation balanced. Now that we've found the solution, let's move on to verifying our answer to make sure we didn't make any mistakes along the way.

Step 3: Verify the Solution

Okay, guys, we've found that x = -115.2, but it's always a good idea to double-check our work to make sure we didn't make any sneaky errors. To verify our solution, we'll substitute -115.2 back into the original equation: -1.5 + x/6 = -20.7. This process is like plugging our answer back into the puzzle to see if it fits. If both sides of the equation are equal after the substitution, then we know our solution is correct. So, let's replace x with -115.2 in the equation:

-1.5 + (-115.2)/6 = -20.7

Now, we need to simplify the left side of the equation. First, we'll divide -115.2 by 6. This gives us -19.2. So, the equation now looks like this:

-1.5 + (-19.2) = -20.7

Next, we add -1.5 and -19.2. This gives us -20.7. So, the left side of the equation simplifies to -20.7. Now, let's compare this to the right side of the original equation, which is also -20.7. We have:

-20.7 = -20.7

Since both sides of the equation are equal, our solution is correct! This verification step is super important because it confirms that we've correctly solved for x. It's like getting the final stamp of approval on our work. By substituting our solution back into the original equation and showing that it holds true, we can be confident that x = -115.2 is indeed the correct answer.

Conclusion

Alright, guys! We've successfully solved for x in the equation -1.5 + x/6 = -20.7. We walked through each step, from isolating the term with x to finally verifying our solution. Remember, the key steps were:

1. Isolating the term with x by adding 1.5 to both sides of the equation.
2. Solving for x by multiplying both sides of the equation by 6.
3. Verifying our solution by substituting -115.2 back into the original equation.

We found that x = -115.2 is the solution that makes the equation true. By following these steps, you can confidently tackle similar algebraic equations. Solving for variables is a fundamental skill in mathematics, and mastering it will open doors to more advanced topics. Always remember to use inverse operations to isolate the variable and to keep the equation balanced by performing the same operations on both sides. And don't forget to verify your solution to ensure accuracy. Math can seem daunting at times, but breaking it down into manageable steps makes it much less intimidating. Practice makes perfect, so keep working on these types of problems, and you'll become a pro in no time. We hope this guide was helpful and that you now feel more confident in your ability to solve for x. Keep up the great work, and happy solving!