Solving For X In 2x + 5 = 15 A Step-by-Step Guide

Hey guys! Let's dive into solving a basic algebraic equation together. We're going to break down how to find the value of 'x' in the equation 2x + 5 = 15. Don't worry, it's super straightforward once you get the hang of it. We'll go through each step, making sure it's crystal clear how we arrive at the correct answer. So, grab your thinking caps, and let's get started!

Understanding the Equation

Before we jump into solving, let's make sure we understand what the equation 2x + 5 = 15 actually means. In simple terms, it's a mathematical statement that says "twice a certain number (x), plus 5, equals 15." Our mission is to figure out what that "certain number" (x) is. This kind of problem falls under the category of basic algebra, which is a fundamental part of mathematics. Algebraic equations are like puzzles, and we're the detectives trying to solve them! In the equation, 'x' is what we call a variable – it's a symbol that represents an unknown value. The numbers 2 and 5 are constants, meaning their values don't change. The number 15 is the result we're aiming for. The plus sign (+) indicates addition, and the equals sign (=) tells us that the expression on the left side of the equation has the same value as the expression on the right side. To solve for 'x', we need to isolate it on one side of the equation. This means we want to get 'x' by itself, so we can see what its value is. We do this by performing operations on both sides of the equation to maintain the balance. Think of an equation like a balanced scale – whatever you do to one side, you must do to the other to keep it balanced. This principle is key to solving algebraic equations accurately. So, with this understanding in mind, let's move on to the next step: isolating the term with 'x'.

Isolating the Term with 'x'

The first step in solving for 'x' is to isolate the term that contains 'x', which in our equation is 2x. Remember, we want to get 'x' by itself on one side of the equation. Currently, we have 2x + 5 = 15. The '+ 5' is what's keeping the 2x from being completely isolated. To get rid of the '+ 5', we need to perform the inverse operation. The inverse of addition is subtraction, so we'll subtract 5 from both sides of the equation. This is crucial because, as we discussed earlier, we need to keep the equation balanced. Subtracting 5 from one side without doing the same to the other would change the equation's meaning and lead to an incorrect solution. So, let's go ahead and subtract 5 from both sides: 2x + 5 - 5 = 15 - 5. On the left side, the '+ 5' and '- 5' cancel each other out, leaving us with just 2x. On the right side, 15 minus 5 equals 10. Now our equation looks like this: 2x = 10. We're making progress! We've successfully isolated the term with 'x'. Now, we just need to get 'x' completely by itself. To do that, we need to deal with the '2' that's multiplying 'x'. Are you ready for the next step? Let's move on to solving for 'x' directly.

Solving for 'x'

Okay, we're almost there! We've got our equation down to 2x = 10. This means "2 times x equals 10." Our goal now is to find out what 'x' is on its own. To do this, we need to undo the multiplication. The inverse operation of multiplication is division. So, to get 'x' by itself, we'll divide both sides of the equation by 2. Remember, it's super important to do the same thing to both sides to keep the equation balanced. If we only divided one side, we'd be changing the whole equation and messing up our solution. So, let's divide both sides by 2: (2x) / 2 = 10 / 2. On the left side, the 2 in the numerator and the 2 in the denominator cancel each other out, leaving us with just 'x'. On the right side, 10 divided by 2 equals 5. So, our equation now reads: x = 5. Hooray! We've found the value of 'x'. It's like cracking a code, isn't it? Now we know that the number that, when multiplied by 2 and then added to 5, equals 15, is 5. But before we celebrate too much, let's do a quick check to make sure our answer is correct. This is a good habit to get into whenever you're solving equations – it's like double-checking your work to avoid any silly mistakes.

Verifying the Solution

Alright, we've found that x = 5, but let's make absolutely sure our answer is correct. The best way to do this is to substitute our value of 'x' back into the original equation and see if it holds true. Our original equation was 2x + 5 = 15. Now, let's replace 'x' with 5: 2(5) + 5 = 15. First, we perform the multiplication: 2 times 5 equals 10. So now we have: 10 + 5 = 15. Next, we add 10 and 5, which gives us 15. So our equation now reads: 15 = 15. Bingo! The equation holds true. This means that our solution, x = 5, is indeed correct. Verifying your solution is a crucial step in problem-solving. It helps you catch any errors you might have made along the way and gives you confidence in your final answer. Think of it as the final piece of the puzzle that confirms everything else fits perfectly. Now that we've verified our solution, we can confidently say that we've solved for 'x'. But let's not stop here! Let's recap the steps we took and talk about why this process works.

Recapping the Steps and Why They Work

Okay, let's take a moment to recap the steps we took to solve the equation 2x + 5 = 15 and, more importantly, understand why these steps work. This isn't just about getting the right answer; it's about understanding the underlying principles of algebra. First, we isolated the term with 'x'. We had 2x + 5 = 15, and we wanted to get the 2x by itself. To do this, we subtracted 5 from both sides of the equation. This works because of the fundamental principle of equality: whatever you do to one side of an equation, you must do to the other to maintain the balance. Subtracting 5 from both sides cancels out the '+ 5' on the left side, leaving us with 2x = 10. Next, we solved for 'x'. We had 2x = 10, which means "2 times x equals 10." To get 'x' by itself, we needed to undo the multiplication. We did this by dividing both sides of the equation by 2. Again, this maintains the balance of the equation. Dividing 2x by 2 gives us 'x', and dividing 10 by 2 gives us 5, resulting in x = 5. Finally, we verified the solution. We substituted x = 5 back into the original equation to make sure it held true. This step is crucial because it helps us catch any errors we might have made. When we plugged in 5 for 'x', we got 2(5) + 5 = 15, which simplifies to 15 = 15, confirming that our solution is correct. The beauty of algebra is that it provides us with a systematic way to solve for unknowns. By understanding the principles of inverse operations and maintaining the balance of the equation, we can confidently tackle a wide range of algebraic problems. So, pat yourselves on the back, guys! You've successfully solved for 'x' and understood the process behind it. Now, let's answer the original question and choose the correct alternative.

Choosing the Correct Alternative

Now that we've meticulously solved the equation 2x + 5 = 15 and found that x = 5, let's circle back to the original question and select the correct answer from the given alternatives. The question presented us with the following options:

A) 5 B) 10 C) 2 D) 7

Based on our step-by-step solution, we've clearly determined that the value of 'x' is 5. Therefore, the correct alternative is A) 5. It's awesome to see how our hard work and careful calculations have led us to the right answer. This process not only helps us solve the specific problem at hand but also builds our confidence and skills in algebra. Remember, guys, mathematics is like a muscle – the more you exercise it, the stronger it gets. So, keep practicing, keep exploring, and keep challenging yourselves with new problems. You've got this! And who knows, maybe next time you'll be the one explaining the solution to someone else.

Final Thoughts

So, there you have it! We've successfully navigated the equation 2x + 5 = 15, found the value of 'x' to be 5, and understood the reasoning behind each step. From isolating the term with 'x' to verifying our solution, we've covered the essential elements of solving basic algebraic equations. Remember, math isn't just about memorizing formulas and procedures; it's about understanding the underlying concepts and developing problem-solving skills. By breaking down complex problems into smaller, manageable steps, we can tackle even the trickiest challenges with confidence. And always remember to double-check your work – verification is key! I hope this step-by-step guide has been helpful and has made solving equations a little less daunting and a lot more fun. Keep practicing, stay curious, and never stop exploring the fascinating world of mathematics! You guys are awesome, and I know you can conquer any math problem that comes your way.