Equivalent Expression To 2(a+3) When A=3? Solve It!

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Hey guys! Let's dive into solving this math problem together. We're going to figure out which expression is equivalent to 2(a+3) when a=3. It might sound a bit tricky at first, but trust me, we'll break it down step by step so it's super easy to understand. So, grab your pencils, and let’s get started!

Understanding the Problem

Before we jump into the options, let's make sure we understand what the problem is asking. We have an expression, 2(a+3), and we know that a is equal to 3. Our mission is to substitute 3 for a in the expression and then simplify it. We then need to match our simplified result with one of the given options. This involves the fundamental concept of substitution in algebra, where we replace a variable (in this case, 'a') with its given value to evaluate the expression. This is a cornerstone of algebraic manipulations and is used extensively in solving equations and simplifying complex expressions. Mastering this skill is crucial for tackling more advanced math problems later on. Think of it like replacing a piece in a puzzle – we're swapping 'a' with the number 3 to see how the expression changes.

Let's Substitute and Simplify

Okay, so the first thing we need to do is substitute a with 3 in the expression 2(a+3). This gives us 2(3+3). Remember the order of operations (PEMDAS/BODMAS)? We need to tackle what's inside the parentheses first. So, 3 + 3 equals 6. Now our expression looks like this: 2(6). What's 2 times 6? It's 12! So, the simplified value of the expression when a=3 is 12. We've successfully substituted the value and simplified the expression. This process highlights the importance of following the order of operations to ensure accurate results. By simplifying, we've transformed the original expression into a single numerical value, which makes it much easier to compare with the answer choices provided. This step-by-step approach helps to avoid errors and ensures we arrive at the correct solution. It's like following a recipe – each step is crucial for the final dish to turn out perfectly!

Analyzing the Options

Now that we know the simplified value of the expression is 12, let's go through the options and see which one matches.

Option A: 2(3)

Option A is 2(3). What's 2 times 3? It's 6. So, Option A equals 6. Does 6 equal 12? Nope! So, we can eliminate Option A. This is a straightforward application of multiplication, but it's crucial to be precise. We're looking for an option that equals 12, and 6 clearly doesn't fit the bill. Eliminating this option brings us one step closer to the correct answer. It's like a process of elimination in a detective novel – we're ruling out suspects one by one!

Option B: 5(3)

Next up is Option B: 5(3). 5 multiplied by 3 is 15. Is 15 equal to 12? Nope, not this one either! We can cross out Option B. This option reinforces the importance of accurate multiplication. Even a small mistake can lead us to the wrong answer. By calculating 5 times 3 correctly, we quickly see that it doesn't match our target value of 12. Our search continues!

Option C: 2(3)+3

Let's look at Option C: 2(3)+3. We need to follow the order of operations here. First, we multiply 2 by 3, which is 6. Then, we add 3. So, 6 + 3 equals 9. Does 9 equal 12? Nope, Option C is not the correct answer. This option tests our understanding of the order of operations (PEMDAS/BODMAS). We need to multiply before we add, and by doing so correctly, we arrive at a value of 9, which is not the solution we're looking for. We're getting closer to the right answer by eliminating these incorrect choices.

Option D: 2(3)+6

Finally, we have Option D: 2(3)+6. Again, let's follow the order of operations. 2 times 3 is 6. Then, we add 6. So, 6 + 6 equals 12! Bingo! Option D is equivalent to our simplified expression. We've found our match! This option demonstrates the importance of meticulously following each step in the order of operations. By correctly multiplying and then adding, we arrive at the value of 12, which confirms that this is the correct answer. It's like the final piece of the puzzle falling into place!

The Correct Answer

So, after analyzing all the options, we've found that Option D, 2(3)+6, is the expression equivalent to 2(a+3) when a=3. We did it! We've successfully solved the problem by substituting, simplifying, and carefully evaluating each option. This process highlights the key skills needed to tackle algebraic expressions. By breaking the problem down into smaller steps, we made it much more manageable and ensured we arrived at the correct solution. Give yourself a pat on the back!

Key Takeaways

  • Substitution is key: Replacing variables with their given values is a fundamental skill in algebra.
  • Order of operations matters: Always follow PEMDAS/BODMAS to ensure accurate calculations.
  • Break it down: Complex problems become easier when you solve them step by step.
  • Check your work: Double-checking your calculations can help you avoid mistakes.

Why This Matters

Understanding how to substitute and simplify expressions is super important in math. It's like the building block for more advanced topics like solving equations, graphing functions, and even calculus! The skills we've used today are not just for solving textbook problems; they're applicable in various real-world scenarios. Think about calculating the cost of items on sale, determining the amount of ingredients needed for a recipe, or even understanding financial investments. Math is all around us, and mastering these fundamental concepts empowers us to tackle everyday challenges with confidence. So, keep practicing and honing your skills – you'll be amazed at what you can achieve!

Practice Makes Perfect

To really nail this down, try practicing with some similar problems. Here's one to get you started:

What expression is equivalent to 3(b-2) when b=5?

See if you can solve it using the same steps we used today. Remember, the key is to substitute, simplify, and then compare! Practice is the key to mastery in any skill, and math is no exception. The more you practice, the more confident and proficient you'll become. Don't be afraid to make mistakes – they're a natural part of the learning process. Each problem you solve strengthens your understanding and builds your problem-solving abilities.

Final Thoughts

I hope this explanation helped you understand how to find the equivalent expression. Math can be fun, especially when you break it down and tackle it step by step. Keep up the great work, guys, and I'll see you in the next math adventure! We've covered a lot of ground in this explanation, from the initial problem setup to analyzing each option and arriving at the correct answer. Remember, the goal is not just to find the solution but also to understand the underlying concepts and techniques. This deeper understanding will enable you to tackle a wider range of problems with greater confidence and skill. So, keep exploring, keep questioning, and keep learning!