Solving Equations: Find The Value Of X
Hey guys! Let's dive into a classic algebra problem. We're going to figure out the solution to the equation: $\frac{x}{4}=-12$. Don't worry, it's not as scary as it looks. We'll break it down step-by-step so you can totally nail it. Solving equations is a super important skill in math, and once you get the hang of it, you'll be able to tackle all sorts of problems. So, let's get started and find the value of x! This kind of problem often pops up in your math classes, and understanding how to solve it is crucial. This will help you with more complex equations later on. Understanding the fundamentals is key to success.
First, what does this equation even mean? Basically, we're trying to find a number (that's x) that, when divided by 4, gives us -12. Our goal is to isolate x on one side of the equation. To do this, we need to get rid of the division by 4. Think of it like a seesaw; we have to keep things balanced. Whatever we do to one side of the equation, we must do to the other side to keep it fair and balanced. This is a fundamental concept in algebra; keeping the equation balanced. To get x alone, we need to do the opposite of dividing by 4, which is multiplying by 4. Multiplying both sides of the equation by 4 cancels out the division on the left side, leaving us with x. This method is a tried and true way to find the solution. The core of solving equations is figuring out what operations undo each other and how to apply them correctly. Let's explore how to solve this equation! This is the first step toward becoming a math whiz. The equation itself might seem simple, but the principles behind it are essential. Ready to level up your math game? Let's go!
Step-by-Step Solution
Alright, let's work through this step-by-step. Remember our equation: $\frac{x}{4}=-12$. Here’s how we're going to solve it. We're going to use the magic of multiplication. Our first move is to multiply both sides of the equation by 4. This gets rid of the fraction and isolates the x on the left side of the equation. Why 4? Because 4 divided by 4 equals 1, and 1 times x is just x. We want to undo the division. Here's what it looks like:
- Multiply both sides by 4: $4 * \frac{x}{4} = 4 * (-12)$
- Simplify: On the left side, the 4 in the numerator and denominator cancel out, leaving us with x. On the right side, 4 times -12 is -48.
- The simplified equation looks like: $x = -48$
See how easy that was, guys? We've successfully isolated x. The equation is now solved, and we have found the value of x. The solution to the equation $\frac{x}{4}=-12$ is x = -48. Pretty cool, huh? This simple trick of multiplying to get rid of the fraction is a lifesaver in algebra. Understanding this process builds a strong foundation. This allows you to tackle more complex equations. Remember, the key is to isolate the variable. Make sure you apply the same operation to both sides of the equation. Make sure you have balance. Once you grasp this concept, you will feel confident. We are almost there, we have one final step to solidify our answer!
Selecting the Correct Answer
Okay, so we've solved the equation. We know that x = -48. Now, let’s go back to the multiple-choice options and find the one that matches our solution. We're looking for the answer choice that says $x = -48$. Here's a look at the options:
A. $x=-3$ B. $x=-48$ C. $x=3$ D. $x=48$
Clearly, the correct answer is B. $x=-48$. Boom! You did it! You have successfully solved the equation and selected the correct answer. Give yourself a pat on the back! This skill is super valuable. It forms the base of many mathematical concepts. Remember, practice makes perfect. Keep solving equations and practicing. The more you practice, the more comfortable you'll become. So, keep up the great work and keep solving. Solving these equations builds confidence. It will prepare you for more complicated problems. We have one last thing we need to do to double check our work.
Verification
Always a good idea, let's double-check our work. Let's make sure our answer, x = -48, is correct. To do this, we're going to substitute -48 back into the original equation and see if it holds true. So, our original equation was: $\frac{x}{4}=-12$. We'll replace x with -48:
Now, let’s simplify the left side. -48 divided by 4 equals -12. So, we get:
Since the left side of the equation equals the right side, our answer is correct. Our solution checks out, guys! We're confident that $x = -48$ is the correct answer. This verification step is a great habit to get into. This allows you to catch any errors and ensures your answer is accurate. It’s like double-checking your work before submitting it. It gives you extra confidence in your answer. Now you can say, you know how to solve this equation! You have learned how to solve the equation. You have the power to solve similar equations.
Conclusion
Awesome work, everyone! You've successfully solved the equation $\frac{x}{4}=-12$ and learned some important math skills. We broke down the problem step-by-step and made sure you understood the logic behind each move. You now know how to isolate a variable using multiplication. You also know how to verify your answers. Remember, practice is key. The more you practice these types of problems, the easier they will become. Keep up the great work and never be afraid to ask for help or review the steps. You've got this, and you're well on your way to mastering algebra. Keep going and keep practicing. You are now equipped with the tools to confidently solve similar problems. Congratulations on another math victory. Keep exploring and keep learning. Math is fun. You have the skills and knowledge to solve these problems! Keep practicing and keep up the amazing work!