Solve For X: A Step-by-Step Guide To (x-16)/5 = 10

Alright, guys! Let's dive into solving a simple algebraic equation. Today, we're going to break down how to find the value of 'x' in the equation (x - 16) / 5 = 10. Don't worry; it's easier than it looks! We'll go through each step carefully, so even if you're just starting with algebra, you'll be able to follow along. So, grab your pencils and notebooks, and let's get started!

Understanding the Equation

Before we jump into solving, it's important to understand what the equation is telling us. The equation (x - 16) / 5 = 10 essentially says that if you take a number 'x', subtract 16 from it, and then divide the result by 5, you'll end up with 10. Our goal is to find out what that original number 'x' is.

In essence, when tackling algebraic equations, it's crucial to grasp the fundamental principles at play. Equations like (x - 16) / 5 = 10 serve as mathematical puzzles, each component playing a vital role in determining the unknown variable, in this case, 'x'. Breaking down the equation into its constituent parts allows us to discern the relationships between the variable and the constants. This understanding forms the bedrock upon which we build our problem-solving strategy. By recognizing that the equation represents a sequence of operations performed on 'x', we can begin to unravel these operations in reverse order to isolate 'x' and ultimately find its value. Furthermore, grasping the concept of equality is paramount; the equation asserts that the expression on the left-hand side is precisely equivalent to the value on the right-hand side. This equivalence enables us to manipulate the equation while preserving its integrity, ensuring that any operations performed on one side are mirrored on the other. Thus, a solid comprehension of the equation's structure and the principles of equality lays the groundwork for a successful resolution.

Step 1: Isolate the Term with 'x'

Our first goal is to isolate the term that contains 'x', which in this case is (x - 16). To do this, we need to get rid of the division by 5. We can accomplish this by multiplying both sides of the equation by 5. Remember, whatever we do to one side of the equation, we must do to the other to keep it balanced.

So, we have:

(x - 16) / 5 * 5 = 10 * 5

This simplifies to:

x - 16 = 50

Now, the equation looks much simpler! This initial step, often referred to as isolating the term with 'x', is a cornerstone of algebraic manipulation. By strategically applying inverse operations, such as multiplying both sides of the equation by 5, we effectively undo the division operation and pave the way for further simplification. It's crucial to emphasize the importance of maintaining balance throughout this process; whatever action is performed on one side of the equation must be mirrored on the other side to preserve the equality. This principle ensures that the solution remains valid and accurate. Moreover, isolating the term with 'x' allows us to focus our attention on the remaining operations that need to be undone in order to ultimately solve for 'x'. By systematically peeling away the layers of complexity, we gradually inch closer to the final solution, making the problem more manageable and less daunting. Thus, mastering the art of isolating terms is a fundamental skill for anyone venturing into the realm of algebra.

Step 2: Isolate 'x'

Now that we have x - 16 = 50, we need to isolate 'x' completely. To do this, we need to get rid of the subtraction of 16. We can do this by adding 16 to both sides of the equation:

x - 16 + 16 = 50 + 16

This simplifies to:

x = 66

And there you have it! We've found the value of 'x'. At this stage, the focus shifts squarely to isolating 'x' entirely, removing any remaining operations that hinder its solo existence on one side of the equation. In our case, we confront the subtraction of 16, which can be elegantly neutralized by adding 16 to both sides of the equation. This maneuver effectively cancels out the subtraction, leaving 'x' standing alone in all its glory. As before, maintaining equilibrium is paramount; the addition of 16 to both sides ensures that the equation remains balanced, preserving the integrity of the solution. Furthermore, this step highlights the power of inverse operations in unraveling mathematical puzzles. By strategically applying the opposite operation to the one impeding 'x', we systematically peel away the layers of complexity until 'x' is finally revealed in its true form. With each step, we draw closer to the ultimate goal of solving for 'x', solidifying our understanding of algebraic principles and enhancing our problem-solving prowess. Thus, mastering the art of isolating 'x' is not just a means to an end but a testament to our growing mastery of mathematical manipulation.

Step 3: Verify the Solution

To make sure our answer is correct, we can plug the value of x we found (which is 66) back into the original equation:

(66 - 16) / 5 = 10

Let's simplify:

(50) / 5 = 10

10 = 10

Since both sides of the equation are equal, our solution is correct! Verifying the solution is the final checkpoint on our journey to solving for 'x', serving as a crucial step to ensure accuracy and confidence in our answer. By plugging the value of 'x' back into the original equation, we put our solution to the ultimate test. In our case, we substitute x = 66 into the equation (x - 16) / 5 = 10 and meticulously simplify each side. If the equation holds true, with both sides yielding the same value, then we can rest assured that our solution is indeed correct. This process not only validates our answer but also reinforces our understanding of the equation and the principles of equality. Moreover, verifying the solution provides an opportunity to catch any errors that may have occurred during the problem-solving process. By double-checking our work, we minimize the risk of accepting an incorrect answer and solidify our grasp of algebraic concepts. Thus, verification is not merely a formality but an integral part of the problem-solving process, instilling confidence in our abilities and ensuring the accuracy of our results.

Conclusion

So, to solve for x in the equation (x - 16) / 5 = 10, we found that x = 66. Remember to always isolate the term with 'x' first, then isolate 'x' itself, and finally, verify your solution to make sure it's correct. With a little practice, you'll be solving algebraic equations like a pro in no time! Keep up the great work, and happy solving!

In conclusion, mastering the art of solving for 'x' in equations like (x - 16) / 5 = 10 is a valuable skill that extends far beyond the realm of mathematics. It cultivates critical thinking, problem-solving abilities, and attention to detail – qualities that are highly sought after in various aspects of life. By following a systematic approach, such as isolating terms, applying inverse operations, and verifying solutions, we can confidently tackle algebraic challenges and unlock their hidden truths. Moreover, the process of solving for 'x' fosters a deeper understanding of mathematical principles, empowering us to approach more complex problems with clarity and precision. So, embrace the journey of learning and practice, for with each equation solved, we sharpen our minds and expand our horizons. As we continue to hone our algebraic skills, we not only gain proficiency in mathematics but also develop a resilient mindset that enables us to overcome obstacles and achieve our goals. Thus, the pursuit of solving for 'x' is not just about finding a numerical answer; it's about cultivating a mindset of curiosity, perseverance, and intellectual growth.