Evaluating Algebraic Expressions Step-by-Step Guide
Hey guys! Today, we're diving into the world of evaluating expressions, and we're going to make it super easy and fun. We'll be focusing on what happens when $x=2$, and we'll tackle a couple of expressions to show you exactly how it's done. Think of it as a mathematical adventure where we unlock the mystery of these equations!
Evaluating -9.2(4-x) for x=2
Let's kick things off with our first expression: -9.2(4-x). Our mission, should we choose to accept it, is to figure out what this expression equals when $x$ is equal to 2. Don't worry, it's not as daunting as it sounds! We'll break it down step by step, making sure everyone's on board.
Step 1: Substitution – The Key to Unlocking the Expression
The very first thing we need to do is substitute the value of $x$ into the expression. In this case, we know that $x=2$, so wherever we see an $x$ in the expression, we're going to replace it with a 2. This is like swapping out a piece in a puzzle – we're just replacing $x$ with its numerical value. So, our expression -9.2(4-x) becomes -9.2(4-(2)). See? We just swapped the $x$ for a 2. Easy peasy!
Step 2: Parentheses First – Following the Order of Operations
Now that we've substituted, it's time to remember our order of operations. You might have heard of the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction), or maybe you know it as BODMAS (Brackets, Orders, Division and Multiplication, Addition and Subtraction). Either way, the message is the same: we need to tackle what's inside the parentheses first. Looking at our expression, -9.2(4-(2)), we see the part inside the parentheses is (4-(2)). This is a simple subtraction problem: 4 minus 2. So, 4 - 2 = 2. We've simplified the expression inside the parentheses, and now we have -9.2(2).
Step 3: Multiplication – The Final Showdown
We're almost there! The last step is to perform the multiplication. We have -9.2 multiplied by 2. When we multiply these two numbers together, we get -18.4. Remember, a negative number multiplied by a positive number gives us a negative result. So, -9.2 multiplied by 2 is indeed -18.4. And there you have it! We've successfully evaluated the expression -9.2(4-x) for $x=2$. The answer is -18.4.
To summarize, evaluating the expression -9.2(4-x) for $x=2$ involves substituting 2 for $x$, simplifying the expression inside the parentheses (4-2), and then performing the multiplication of -9.2 and 2. This methodical approach ensures accuracy and clarity in solving the problem. The result, as we found, is -18.4. This process highlights the importance of the order of operations and the careful application of arithmetic principles to arrive at the correct solution. By following these steps, you can confidently tackle similar expressions and deepen your understanding of algebraic evaluation. Remember, practice makes perfect, so keep exploring and experimenting with different expressions to hone your skills!
Evaluating -36.8 + 9.2x for x=2
Alright, let's move on to our second expression: -36.8 + 9.2x. This one looks a little different, but don't worry, the same principles apply. We're still going to substitute $x=2$ and follow the order of operations to find the value of the expression. Let's jump right in!
Step 1: Substitution – Replacing x with 2
Just like before, our first move is to substitute. We're replacing $x$ with 2 in the expression -36.8 + 9.2x. This gives us -36.8 + 9.2(2). Notice how we've put the 2 in parentheses next to the 9.2? This indicates that we're going to multiply 9.2 by 2. Substitution is a fundamental step in evaluating expressions, and it's crucial to get it right. Make sure you're carefully replacing the variable with its given value.
Step 2: Multiplication – Handling the Product Term
Following the order of operations, we need to handle multiplication before we tackle addition. In our expression, -36.8 + 9.2(2), we have a multiplication operation: 9.2 multiplied by 2. When we perform this multiplication, we get 18.4. So, 9.2 multiplied by 2 equals 18.4. Now our expression looks like this: -36.8 + 18.4. We've simplified the multiplication part, and we're one step closer to the final answer.
Step 3: Addition – Bringing It All Together
Finally, we come to the addition part. We have -36.8 + 18.4. This is where we need to be careful with our signs. We're adding a positive number (18.4) to a negative number (-36.8). Think of it like this: we're starting at -36.8 on the number line and moving 18.4 units to the right. When we do the math, we find that -36.8 + 18.4 = -18.4. So, the value of the expression -36.8 + 9.2x when $x=2$ is -18.4. Awesome job, guys! We've cracked another mathematical code.
In summary, evaluating the expression -36.8 + 9.2x for $x=2$ requires substituting 2 for $x$, performing the multiplication of 9.2 and 2, and then adding the result to -36.8. This methodical approach, consistent with the order of operations, leads us to the solution of -18.4. This example reinforces the importance of careful attention to detail, especially when dealing with negative numbers. By mastering these steps, you build a strong foundation for tackling more complex algebraic problems and enhancing your mathematical proficiency. Remember, understanding the process is key, so keep practicing and refining your skills!
Conclusion: Mastering the Art of Evaluating Expressions
So, there you have it! We've successfully evaluated two different expressions for $x=2$. We've seen how substitution and the order of operations are our best friends in this mathematical adventure. Remember, evaluating expressions is a fundamental skill in algebra, and it's something you'll use again and again. The more you practice, the more confident you'll become. Keep exploring, keep experimenting, and most importantly, keep having fun with math! You've got this!
