Solving (x - 4) = 14: A Step-by-Step Guide
Hey guys! Let's break down this math problem together. We're going to solve the equation (x - 4) = 14. Don't worry, it's easier than it looks! We will use a step-by-step approach, perfect for anyone who needs a little help with their algebra. Our main goal is to isolate 'x' on one side of the equation so we can find its value. Grab your pencils, and let's dive in!
Understanding the Basics
Before we jump into solving, let's make sure we understand what the equation is telling us. The equation (x - 4) = 14 means that there's a number, which we're calling 'x', and when you subtract 4 from it, you get 14. Our mission is to figure out what that number 'x' is. In essence, we are reversing the subtraction to find the original number. Equations like these are fundamental in algebra, and mastering them will help you tackle more complex problems down the road. Remember, the key is to keep both sides of the equation balanced. Whatever operation you perform on one side, you must also perform on the other side to maintain the equality. This principle ensures that the value of 'x' remains consistent and accurate.
Think of it like a balanced scale. The left side (x - 4) must always weigh the same as the right side (14). If you add or subtract something from one side, you need to do the same on the other to keep the scale balanced. This concept is crucial for solving any algebraic equation. Understanding this balance makes the process much more intuitive and less intimidating. So, with our balanced scale analogy in mind, let’s move on to the actual steps of solving the equation and finding the value of 'x'. Keeping the equation balanced will guide us to the correct answer.
Also, keep in mind that 'x' is just a placeholder. We could have used any letter, like 'y' or 'z', but 'x' is commonly used in algebra. The important thing is that it represents an unknown value that we need to find. Understanding this simple concept can make algebra less daunting. Now that we have a solid understanding of the basics, we can confidently move forward to solving the equation. Remember, practice makes perfect, so don't be discouraged if it takes a few tries to get the hang of it. With each problem you solve, you'll build your confidence and skills in algebra.
Step-by-Step Solution
Alright, let's get to the fun part – solving for 'x'! Here’s how we do it:
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Isolate x: Our goal is to get 'x' by itself on one side of the equation. To do this, we need to get rid of the '- 4' that’s attached to it. The opposite of subtracting 4 is adding 4. So, we're going to add 4 to both sides of the equation. Adding the same number to both sides keeps the equation balanced, which is super important.
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Perform the Addition: (x - 4) + 4 = 14 + 4 This simplifies to: x = 18
And that's it! We found that x = 18. Wasn't so hard, was it? By adding 4 to both sides, we successfully isolated 'x' and discovered its value. Now, let’s quickly verify our answer to ensure we didn't make any mistakes along the way. Verifying your solution is always a good practice, especially when you're just starting to learn algebra. It helps you catch any errors and reinforces your understanding of the process. To verify, simply plug the value of 'x' back into the original equation and see if it holds true.
Verification
To make sure we got the right answer, let's plug x = 18 back into the original equation:
(x - 4) = 14 (18 - 4) = 14 14 = 14
Yep, it checks out! Both sides of the equation are equal, so we know that x = 18 is the correct solution. Verifying your answer is a great habit to get into because it confirms that you followed the steps correctly and didn't make any arithmetic errors. It’s like a little safety net that ensures you're on the right track. Plus, it gives you confidence in your solution. If the equation didn't balance out after plugging in your value for 'x', that would be a sign that you need to go back and review your steps to find the mistake. So, always take a moment to verify your solutions—it's worth the extra effort!
Conclusion
So, the answer to the equation (x - 4) = 14 is x = 18. You did it! Remember, the key to solving these types of equations is to isolate the variable by performing the opposite operation on both sides of the equation. Keep practicing, and you'll become a pro at solving algebraic equations in no time! Keep in mind that algebra is a building block for more advanced math, so mastering these basics is super important. Don't be afraid to ask for help if you get stuck, and remember to always double-check your work. With a little bit of effort and practice, you'll be solving even the most complex equations with ease. And hey, if you ever need a refresher, just come back to this guide. We're here to help you succeed in math! Good job, and keep up the great work!
Math can be a lot of fun once you get the hang of it, so embrace the challenge and enjoy the process of learning. And remember, every math problem you solve is a step forward in your mathematical journey. So, keep stepping, keep learning, and keep solving! You've got this!