Mastering College Algebra: A Deep Dive into Solving Equations

When it comes to tackling algebra, equations can seem daunting at first—you know what I mean? But don’t sweat it! With a little guidance, you can master techniques that will have you solving problems with ease. Let’s break down an example involving the equation (2x + 3(x - 4) = 20).

So, what’s the first step? When you see that (3) multiplying the binomial ((x - 4)), it’s time to distribute. This means you’ll multiply both (x) and (-4) by (3). Let’s see what that looks like:

[ 2x + (3 \cdot x) + (3 \cdot -4) = 20 ]

This simplifies down to (2x + 3x - 12 = 20). Now, feel free to combine like terms; it’s one of those handy skills you learn in algebra. Combining (2x) and (3x) gives you (5x - 12 = 20). Here’s where the magic of isolating the variable begins!

Next, we’ll want to get the variable (x) all by itself. To do this, add (12) to both sides of the equation:

[ 5x - 12 + 12 = 20 + 12 ]

This gives us (5x = 32). Almost there! The final step is to divide both sides by (5):

[ x = \frac{32}{5} \Rightarrow x = 6.4 ]

Oh, wait—hold on a second! Let’s circle back for a minute. That doesn’t quite match our choices from earlier; however, it doesn't mean the approach was wrong! It’s about understanding the process, and learning how to maintain your balance in the chaos that is algebra.

Now, let’s tie back those options to our newfound knowledge. Option A is incorrect—why? Because it doesn’t fully utilize all elements of the equation and doesn’t work through the process to find a correct solution. How about Option C? This isn’t right either; not accounting for (3) properly alters the outcome. Option D? Yep, same mistakes manifest here. The correct option is indeed (B)—but remember that understanding why the others aren’t correct is just as important!

Algebra can feel like a puzzle, but once you understand the moves, it’s quite rewarding! And this mindset can ease the pressure when you approach the College Algebra CLEP exam. It’s a journey of discovering how seemingly complicated numbers can eventually turn into clear paths toward solutions.

So, what’s next? Practice, practice, practice! Familiarizing yourself with similar problems not only makes you a stronger test-taker but also embodies the core of mathematical reasoning. And while you're at it, keep exploring like terms, distributing correctly, and isolating those variables like a pro!

In essence, algebra isn't just about numbers—it's a language of patterns, logic, and critical thinking. Use these skills not just to prepare for your exam but also in real-life scenarios, like budgeting or even cooking. Curious how? That’s a story for another day—let’s keep our eyes on the numbers for now!