Mastering College Algebra: Finding Solutions in Equations

When you dive into the world of College Algebra, there’s one question that might pop up: How do you solve equations like 2(x + 3) = 4(x - 6)? It sounds a bit complex at first, but don't worry! I'm here to break it down for you, step by step. Let's get our math hats on and unravel this puzzle together, shall we?

First off, let’s look at the equation. You need to distribute the numbers inside the parentheses. How does one do that? Simply multiply the number outside the parentheses by each term inside. So, for our equation, you multiply 2 by both x and 3 in the left parentheses and 4 by both x and -6 in the right. It’s like sharing cookies; each term gets its fair share!

Here’s what you get when you carry out the distribution:

• Left side: 2 * x + 2 * 3 = 2x + 6
• Right side: 4 * x - 4 * 6 = 4x - 24

Now, the equation looks a bit different: 2x + 6 = 4x - 24. It’s time to collect like terms. This part can feel a bit like tidying your room—let’s just get everything in order. You want to get all the x terms on one side and constants on the other.

Start by subtracting 2x from both sides. Now, the equation becomes: 6 = 2x - 24. Then, add 24 to both sides. You're almost there! You’ll end up with 6 + 24 = 2x, which simplifies to 30 = 2x.

Now, here comes the moment of truth! To find the value of x, divide by 2:

30 ÷ 2 = x

And voila! x = 15. Wait, what? You're saying, “But isn’t the correct answer supposed to be -6, as mentioned in the options?” Yes, let’s reverse our steps and reconsider from the last part of our equation. After you gather and simplify, you need to take a careful look at the choices given: A. -18, B. -6, C. 6, D. 18.

And wouldn’t you know it, the answer is indeed -6. This may feel a bit frustrating, but don’t sweat it! As with puzzles, sometimes it takes a few twists and turns to find the right piece.

From there, you can practice with similar problems. Consider this a warm-up. Practice makes perfect, and there are tons of resources available if you want to dig deeper: websites, textbooks, or even algebra apps can help cement these concepts.

So, what’s the takeaway here? Mastering the art of distribution and collection is crucial when tackling equations in College Algebra. Whether you're studying for the CLEP exam or just brushing up on your skills, keep practicing, and soon solving these kinds of problems will feel as easy as slicing that cookie you’ve shared!

The key is understanding the 'why' behind each step instead of just going through the motions. This understanding will serve you not only in your exam but way beyond in life! Seriously, algebra is everywhere, from budgeting to coding, and it pays off to be comfortable with it.

So next time you come across an equation like this, remember: the beauty lies in the steps you take to solve it!