Solve: X - A + X - B - 20 If X=3, A+b=25

Hey guys! Let's dive into this math problem where we need to find the value of x - a + x - b - 20 given that x = 3 and a + b = 25. It might look a bit intimidating at first, but don't worry, we'll break it down step by step so it's super easy to understand. We're going to make sure every bit of it makes sense, and you'll be a pro at solving these kinds of problems in no time! So, stick with me, and let's get started!

Understanding the Problem

First off, let's make sure we totally get what the problem is asking. We've got this expression, x - a + x - b - 20, and we need to figure out what number it equals. But, we're not just pulling numbers out of thin air – we've got some clues! We know that x is 3, and when you add a and b together, you get 25. These are like our secret ingredients to solving the puzzle. The trick here is to use these clues to simplify the expression and find our answer. Think of it like a detective game, where the clues lead us to the final solution. We'll use these pieces of information to navigate through the math and nail the correct value. So, with our detective hats on, let's see how these pieces fit together!

Breaking Down the Given Information

Okay, let's really dig into what we already know. We've got two super important pieces of info here: x = 3 and a + b = 25. These aren't just random facts; they're the keys that unlock our solution. The first one, x = 3, is pretty straightforward. It tells us exactly what x is, no guesswork needed. This is like finding a marked treasure on a map – we know exactly where to go! The second piece, a + b = 25, is a little more interesting. It tells us that if we were to add the numbers a and b together, we'd get 25. But it doesn't tell us what a or b are individually. This is like having a recipe where you know the total amount of two ingredients, but not how much of each to use. We're going to use both of these facts to simplify our expression, so it's important we understand them completely. With these in hand, we're ready to start simplifying!

Simplifying the Expression

Now, let's roll up our sleeves and get to the real work – simplifying the expression! We've got x - a + x - b - 20, and it might seem a bit jumbled, but we can totally make it easier to handle. The first thing we're going to do is rearrange the terms a bit. Think of it like organizing your desk – putting things where they make the most sense. We can group the x terms together because they're like buddies, and they'll work well together. So, we can rewrite our expression as x + x - a - b - 20. See? Already it looks a little cleaner. Next up, let's combine those x terms. x + x is just 2x, right? So now we've got 2x - a - b - 20. We're making progress! This is like turning a tangled mess of yarn into a neat, manageable ball. We're not done yet, but we're definitely on the right track. Let's keep going and see how much simpler we can make this.

Grouping Like Terms

Alright, let's get even more organized with our expression. We've already combined the x terms, which is awesome, but we can do more. Look at the - a - b part. Notice anything? It's like we're subtracting both a and b. This is a clue that we can actually group these together! Think of it like combining all your debts into one lump sum – it makes it easier to see the big picture. We can rewrite - a - b as - (a + b). It's the same thing, just written a bit differently. Now our expression looks like this: 2x - (a + b) - 20. See how we've put a + b inside parentheses with a minus sign in front? This is super handy because we actually know the value of a + b! Remember, it's 25. Grouping like terms like this is a smart move because it lets us use the information we have to make our expression even simpler. We're turning our puzzle into something much easier to solve, one step at a time!

Substituting the Values

Okay, this is where the magic really happens! We're going to take those values we know – x = 3 and a + b = 25 – and plug them into our simplified expression. It's like we're finally putting the right keys into the right locks. Our expression is 2x - (a + b) - 20, right? So, wherever we see an x, we're going to replace it with a 3, and wherever we see (a + b), we're going to swap it out for a 25. This is called substitution, and it's a super powerful tool in math. It lets us turn abstract letters into actual numbers, which we can then work with. So, let's do it! When we substitute, our expression becomes 2 * 3 - 25 - 20. See how the x turned into a 3 and the (a + b) turned into a 25? Now we're talking! We've got a string of numbers and operations, and we're ready to crunch them and find our final answer. Let's go!

Replacing x and (a + b)

Let's zoom in a bit more on this substitution process, just to make sure we're crystal clear on what's happening. We started with 2x - (a + b) - 20, and we knew that x is 3 and a + b is 25. So, when we substitute, we're not just randomly swapping numbers; we're carefully replacing each variable with its known value. It's like we're filling in the blanks in a sentence. The 2x becomes 2 * 3 because that's what 2x means – 2 times whatever x is. And the (a + b) becomes 25 because that's the total we get when we add a and b together. We're not changing the meaning of the expression; we're just rewriting it in terms of numbers. This is a crucial step because it gets us from algebra, where we're working with letters, to arithmetic, where we're working with numbers. And once we're in the land of numbers, we can use our regular math skills to solve the problem. So, with our substitutions made, we're all set to do the arithmetic!

Calculating the Final Value

Alright, we've done the hard part – simplifying and substituting. Now comes the really satisfying bit: calculating the final value! We've got 2 * 3 - 25 - 20, and it's just a matter of following the order of operations to get our answer. Remember PEMDAS or BODMAS? We need to do multiplication before addition and subtraction. So, first up, let's tackle 2 * 3. That's easy peasy – it's 6. Now our expression looks like this: 6 - 25 - 20. We're in the home stretch! Next, we just need to do the subtraction. We're subtracting from left to right, so let's start with 6 - 25. That gives us -19. Now we've got -19 - 20. And finally, -19 - 20 is -39. Boom! We've done it! The value of x - a + x - b - 20, when x = 3 and a + b = 25, is -39. High fives all around!

Step-by-Step Arithmetic

Let's break down the arithmetic even further, just to make sure every single step is crystal clear. We've got 6 - 25 - 20, and we need to subtract in the right order. When we're dealing with just addition and subtraction, we go from left to right, just like reading a sentence. So, first up is 6 - 25. This is like starting with 6 bucks and then owing someone 25 bucks. You're going to end up in the hole, right? The answer is -19. We're in negative territory now! It's super important to get the sign right here – a positive or negative sign can make a huge difference in the final answer. Now we've got -19 - 20. This is like owing 19 bucks and then owing another 20 bucks. You're digging a deeper hole! To figure this out, we add the numbers (19 and 20) and keep the negative sign. So, 19 + 20 is 39, and with the negative sign, we get -39. And that's our final answer! We've walked through every single step, making sure we didn't miss anything. You guys are math superstars!

Conclusion

Wow, we did it! We successfully calculated the value of x - a + x - b - 20 when x = 3 and a + b = 25. We took a problem that might have seemed a bit tricky at first, and we broke it down into manageable steps. We started by understanding the problem, then we simplified the expression by grouping like terms. After that, we substituted the values of x and (a + b), and finally, we did the arithmetic to find our answer: -39. This is a fantastic example of how you can tackle any math problem by taking it one step at a time. Remember, math is like a puzzle, and every piece of information is a clue. By carefully putting the pieces together, you can solve anything! So, keep practicing, keep asking questions, and most importantly, keep having fun with math! You've got this!