Mastering College Algebra: Simplifying Expressions with Confidence

When it comes to mastering college algebra, understanding how to simplify expressions is a foundational skill you don't want to overlook. Imagine this: you’re sitting down with your books, ready to conquer that CLEP exam, and a question pops up asking you to simplify the expression 2(3x-4)+5(x+2). You’re thinking, “What do I even do here?” But fear not! We’re diving into the steps that will empower you to tackle such problems easily and confidently.

Let’s break it down. First, the expression we have is 2(3x-4)+5(x+2). This doesn’t look too scary, does it? If you’ve got a good grasp of the distributive property, you're already on the right track! Here’s the thing: the distributive property is your best friend when you’re simplifying expressions. It tells you to multiply the term outside the parentheses by each of the terms inside.

So, starting with the first part, we multiply 2 by both 3x and -4. That gives us 6x - 8. Easy, right? Now let’s move on to the second part. We distribute 5 to both x and 2 in the parentheses. This yields 5x + 10. So far so good!

Now we combine our results. We have 6x - 8 + 5x + 10. The next step involves gathering like terms. Combining 6x and 5x, we get 11x. As for the constants, -8 and +10 combine to give us +2. So, the final simplified expression becomes 11x + 2.

Now, wait a minute—hold on! If I said the answer was 18x-6, we’ve got a little mix-up on our hands, haven’t we? No need to panic. The correct answer here is actually not in the options provided; it’s 11x + 2. This means we need to carefully check our work and options when preparing for your college algebra tasks to make sure you don’t miss any details.

Looking closely at the incorrect options, we can see why they fell short:

• Option A incorrectly applies the distributive property by not subtracting 8 correctly.
• Option B throws in an extra term that isn’t in our original expression, which can definitely lead you astray.
• Option C doesn’t handle the 5 multiplication properly and misses combining like terms effectively.

What’s the takeaway here? Master the distributive property and practice combining like terms to gain fluency in simplifying expressions. It’s like building the blocks for your algebra foundation! Just imagine how satisfying it will feel to tackle algebra questions with ease—just like riding a bike!

Plus, keeping your skills sharp isn’t just about the exam. Whether you're pursuing advanced mathematics or even just trying to understand financials for a personal project, these skills are incredibly versatile. So, don’t shy away from grabbing a few extra practice problems here and there!

At the end of the day, the more you engage with these concepts, the easier they’ll be to navigate. So take a deep breath, grab that pencil, and let’s get simplifying!