Evaluate (p+q)(2) Using Tables: A Step-by-Step Guide
Hey guys! Let's dive into a fun math problem where we need to figure out the value of (p+q)(2) using some tables. This might sound a bit intimidating at first, but trust me, it's super manageable once we break it down. We'll go through it step by step, making sure everyone understands exactly what's going on. So, grab your thinking caps, and let's get started!
Understanding the Problem
Before we jump into solving, let's make sure we understand what the question is asking. We're given two tables. The first table shows the values of a function p(x) for different values of x, and the second table does the same for a function q(x). Our mission, should we choose to accept it (and we do!), is to find the value of the combined function (p+q)(2). What does this mean? Well, it simply means we need to add the values of p(2) and q(2) together. Think of it like this: we're finding out what p does when x is 2, finding out what q does when x is 2, and then adding those results. Easy peasy, right? But before we start adding, we need to extract the correct information from the tables. So let's look at those tables closely and see what they tell us about p(2) and q(2). Remember, the key here is accuracy. We need to make sure we're pulling the right numbers from the tables; otherwise, our final answer won't be correct. This foundational understanding is crucial. Without it, we're just guessing, and nobody wants to guess in math! We want to be confident in our answers, and that confidence comes from truly understanding the problem.
Extracting Values from the Tables
Alright, let's put our detective hats on and extract the crucial information from the tables. We need to find p(2) and q(2). Looking at the first table, which shows the values for p(x), we need to find the row where x is 2. Can you spot it? Awesome! Now, what's the corresponding value for p(x) in that row? It's 3! So, we know that p(2) = 3. Now, let's move on to the second table, the one showing values for q(x). Again, we're looking for the row where x is 2. Found it? Great! What's the value of q(x) in this row? It's -2. So, we've discovered that q(2) = -2. See how we carefully read the tables? It's like reading a map β you need to follow the signs (or in this case, the numbers) carefully to get to your destination. Now that we have our two key pieces of information, p(2) and q(2), we're ready for the next step. We've done the hard work of finding the individual values; now, it's just a matter of putting them together. Think of this like gathering ingredients for a recipe. We've got our flour and sugar (our p(2) and q(2)), and now we're ready to bake (solve the problem!). Remember, double-checking your extracted values is always a good idea. A small mistake here can throw off the whole calculation.
Calculating (p+q)(2)
Okay, we've reached the fun part β the actual calculation! We know that (p+q)(2) means p(2) + q(2). And we've already figured out that p(2) = 3 and q(2) = -2. So, now it's just a simple addition problem: 3 + (-2). What's 3 plus negative 2? It's 1! So, (p+q)(2) = 1. Ta-da! We've solved it! See, it wasn't so scary after all. We took a seemingly complex problem and broke it down into smaller, more manageable steps. That's the secret to success in math β and in life, really. Breaking things down makes them less overwhelming and easier to tackle. We've successfully navigated the tables, extracted the necessary values, and performed the addition. Pat yourselves on the back, guys; you've earned it! But let's not stop here. It's always a good idea to double-check our work, just to be extra sure. There's a famous saying in mathematics: "The best way to learn math is to do math." So, let's reflect on the process we've used and solidify our understanding.
Double-Checking Our Work
It's super important to double-check our work in math, just like it's important to proofread an essay or check the ingredients when you're baking. We want to make sure we haven't made any silly mistakes along the way. So, let's quickly run through our steps again. First, we identified that we needed to find p(2) and q(2) from the tables. Then, we carefully looked at the tables and found that p(2) = 3 and q(2) = -2. Finally, we added those values together: 3 + (-2) = 1. Does everything still look good? Awesome! Another way to double-check is to think about the problem logically. Does our answer make sense in the context of the question? In this case, we were adding two values together, one positive and one negative. The result, 1, is a positive number, which seems reasonable given the numbers we were working with. This kind of logical check can often catch errors that might slip past a simple re-calculation. Remember, double-checking isn't about distrusting your own abilities; it's about being thorough and ensuring accuracy. It's a habit that will serve you well in mathematics and beyond. It's like a safety net β it's there to catch you if you stumble.
Conclusion
Alright, guys, we did it! We successfully found the value of (p+q)(2) using the tables. We broke down the problem, extracted the necessary information, performed the calculation, and even double-checked our work. You're all math superstars! The key takeaway here is that even complex-looking problems can be solved by breaking them down into smaller, more manageable steps. Remember to read the problem carefully, understand what's being asked, and take your time. And don't forget to double-check your work! This type of problem is a great example of how math can be like a puzzle. Each piece of information is a clue, and by putting the clues together, we can find the solution. The satisfaction of solving a math problem is like the feeling of completing a jigsaw puzzle β everything clicks into place, and you get a sense of accomplishment. So, keep practicing, keep exploring, and keep enjoying the world of math! You've got this!