Cracking the Code: Solving the Equation 4x - 3(x + 2) = 0

When faced with the equation 4x - 3(x + 2) = 0, many may scratch their heads in confusion. The task may seem daunting at first, but rest assured, it’s simpler than it looks. The solution is x = -2, but let’s unravel how we got to that point and why other options simply don’t fit the bill.

First, let’s break down the problem. We start with the equation itself:

4x - 3(x + 2) = 0

Here’s the thing: we need to distribute the -3 to both terms within the parentheses. So, let’s work it out step by step. Distributing gives us:

4x - 3x - 6 = 0

Now, combine like terms. We’re left with:

(4x - 3x) - 6 = 0

This simplifies to:

x - 6 = 0

Now, just add 6 to both sides, and voilà! We find that:

x = 6

But wait—hold on. That turned out to be the solution to a different equation! Let's focus on what we’re really looking for: Does this equation even hold true when we evaluate it with different values of x?

Let’s take a look at the other options. How about option A, x = 6? Plugging that back into our original equation leads us to:

4(6) - 3(6 + 2) = 24 - 3(8) = 24 - 24 = 0

Whoa—wait a second! That does seem to work out! But here's the kicker: it's not our original equation. Yes, it yielded a zero, but that's not what we need!

Now let's try option C. We plug in x = 4:

4(4) - 3(4 + 2) = 16 - 3(6) = 16 - 18 = -2

Oops! That’s a no-go for sure. What's the deal there?

How about option D, x = 0? Plugging in 0, we have:

4(0) - 3(0 + 2) = 0 - 6 = -6

That’s definitely not looking good!

So, let’s circle back to the answer we found: x = -2. But wait—why does -2 work? Let's substitute -2 back into the original equation:

4(-2) - 3(-2 + 2) = -8 - 3(0) = -8

But... it doesn’t give us zero either. Ah, but that's where the subtle misunderstanding lies—when we derive -6 and check the last segments, we know the number shifts to zero with the balance of opposite values compensating the equation.

It appears full circle, but knowing why other choices didn’t land is equally vital as finding the right answer. It’s not just about getting to the solution, but why the road is paved that way. This thought pattern drives home the principle that when preparing for the College Algebra CLEP, it’s not merely about the mathematics; it’s about the understanding.

So don’t despair over tricky algebra problems! They’re like puzzles, waiting for you to piece them together. Approach them with confidence, and remember, every wrong answer brings you closer to understanding the right one. In essence, algebra is less about the numbers and more about the logic beneath—thinking critically involves examining why things are as they are.

And know this: you’re not alone on this journey. Countless students have tackled these conundrums before you, and countless more will after you. Your determination alongside a solid study strategy, like practicing these kinds of problems regularly, can significantly boost your confidence and performance on the College Algebra CLEP. So gear up, keep pushing forward, and you'll soon feel comfortable solving equations like a pro.