Solve: Double A Number Plus 5 Equals 10
Hey everyone! Let's dive into a fun math problem today. We're going to break down how to solve the equation where “double a number, then add five, and it equals ten.” This kind of problem is super common in algebra, and once you get the hang of it, you’ll be solving them like a pro. We will use a step-by-step approach to tackle this problem, making it super easy to understand.
Understanding the Problem
First off, let's make sure we really get what the problem is asking. When we see “double a number,” what does that mean mathematically? Exactly! It means we're multiplying some mystery number by two. We often use a variable, like 'x', to stand in for this mystery number. So, “double x” is just 2 * x, or more simply, 2x. Then, we're adding five to this doubled number. So now we have 2x + 5. And the problem says this whole thing equals ten. So, our complete equation looks like this: 2x + 5 = 10. Writing it out like this is the first big step. It turns the words into math we can actually work with. Think of it like translating from one language to another – we’re translating from English to Math! And why is this so important? Because once we have the equation written down, we've got a clear roadmap for how to find our mystery number. We know exactly what operations we need to undo to get 'x' all by itself on one side of the equation. That's the goal: to isolate 'x'. Once we do that, we'll know what number 'x' is, and we’ve solved the problem! So, always remember, breaking down the words and turning them into a neat mathematical equation is key to cracking these kinds of problems. It's like having the secret code to unlock the answer!
Step 1: Isolate the Term with the Variable
The heart of solving any equation like this is to get our variable, 'x', all alone on one side. It's like giving 'x' its own private island! To do this, we need to peel away everything else that's hanging out with 'x'. In our equation, 2x + 5 = 10, 'x' is currently hanging out with a '2' (it’s being multiplied by 2) and a '+ 5' (we're adding five). We need to deal with that '+ 5' first. Think of it like this: we're reverse-engineering the equation. We need to undo what's been done to 'x', but in the opposite order. So, instead of adding 5, we're going to subtract 5. But here’s the golden rule of equations: whatever you do to one side, you absolutely must do to the other side. It's like a seesaw – you need to keep it balanced! So, we subtract 5 from both sides of the equation. This gives us: 2x + 5 - 5 = 10 - 5. Now, let's simplify. On the left side, +5 and -5 cancel each other out – poof, they're gone! That leaves us with just 2x. On the right side, 10 - 5 is simply 5. So, our equation now looks much cleaner: 2x = 5. See how we're getting closer to having 'x' all by itself? We've successfully isolated the term with the variable. We've cleared away the '+ 5', and now it's just '2x' versus '5'. This is a huge step forward. We're halfway there! The next step is to deal with that '2' that's still clinging to 'x'.
Step 2: Solve for the Variable
Okay, we've made some great progress! We've got our equation down to 2x = 5. Now, the final step in getting 'x' all by itself is to deal with that '2' that's multiplying it. Remember, 2x really means 2 * x. So, to undo multiplication, we need to do the opposite operation: division. We're going to divide both sides of the equation by 2. Why both sides? Because, you guessed it, we need to keep the equation balanced! Think of it like evenly splitting a pizza – if you cut one slice bigger, the other slices need to adjust to keep it fair. So, we divide both sides by 2, giving us: (2x) / 2 = 5 / 2. Let's simplify. On the left side, the '2' on top and the '2' on the bottom cancel each other out. Just like before, poof! They're gone. This leaves us with 'x' all by itself – exactly what we wanted! On the right side, 5 / 2 is 2.5. So, our equation now proudly declares: x = 2.5. We did it! We've solved for 'x'. We found the mystery number. Double 2.5, which is 5, and then add 5, and you get 10. It works perfectly! This step is the culmination of all our hard work. We took a word problem, turned it into an equation, and then systematically peeled away the layers until we revealed the value of 'x'. And that, my friends, is the magic of algebra!
Checking Your Answer
Before we do a victory dance, there's one super important step we should always take: checking our answer. It's like proofreading a paper or taste-testing a cake – we want to make sure everything is perfect! So, how do we check if x = 2.5 is the right answer? We simply plug it back into our original equation: 2x + 5 = 10. We replace 'x' with 2.5, giving us: 2 * 2.5 + 5. Now, we just need to do the math and see if it equals 10. First, 2 * 2.5 is 5. So, we have 5 + 5. And what does that equal? You guessed it: 10! Our equation checks out. The left side equals the right side. This means we can be super confident that x = 2.5 is indeed the correct answer. Checking your answer is not just a formality; it's a powerful way to catch any little mistakes you might have made along the way. Maybe you added instead of subtracted, or maybe you divided wrong. By plugging your answer back in, you give yourself a chance to spot those errors and correct them. It's like having a built-in safety net. Plus, let's be honest, it feels really good to see that your answer works! It's like getting a gold star on your math homework. So, always, always, always check your answer. It's the mark of a true math whiz!
Real-World Applications
So, we've cracked the code of this equation, but you might be thinking, “Okay, that's cool, but when am I ever going to use this in real life?” Well, you might be surprised! Algebra, and solving equations like this, is actually used all the time in everyday situations. Let's think about a few examples. Imagine you're planning a party. You know you want to spend a certain amount of money in total, and you have some fixed costs, like the venue rental. You also want to buy snacks, and each snack costs a certain amount. You can use an equation just like this one to figure out how many snacks you can afford! The total cost would be like the '10' in our equation, the venue rental would be part of the '+ 5', and the number of snacks you can buy would be the 'x'. Or, let's say you're trying to save up for something, like a new video game or a concert ticket. You already have some money saved, and you're earning more each week. You can use an equation to figure out how many weeks it will take you to reach your goal. The total amount you need would be the '10', the money you already have would be the '+ 5', and the number of weeks you need to save would be the 'x'. See? Algebra is everywhere! It's not just about abstract numbers and symbols; it's about solving real-world problems. The more comfortable you get with solving equations, the better you'll be at figuring out all sorts of things in your life, from managing your money to planning events to even understanding scientific concepts. So, keep practicing, keep exploring, and keep seeing the math in the world around you!
Conclusion
Alright, guys, we've done it! We've successfully solved the equation where “double a number, then add five, equals ten.” We broke down the problem, turned it into a mathematical equation, isolated the variable, and found our answer. And, just as importantly, we learned why this kind of math is useful in the real world. Remember, the key to tackling these problems is to take them step by step. Don't get overwhelmed by the whole thing at once. Break it down, write it out, and take it one piece at a time. And don't forget to check your answer! Math is like a puzzle, and every equation is a new challenge. The more you practice, the better you'll get at seeing the patterns and finding the solutions. So, keep those math muscles flexed, and keep exploring the wonderful world of numbers and equations. You've got this!
