Understanding the Solution for x in 4x - 3 = 9

When you first look at the equation (4x - 3 = 9), it might seem a bit daunting, but take a breath—solving for x isn’t as tricky as it appears. Let's break it down, step by step, in a way that makes sense and gets you prepped for your College Algebra CLEP Exam.

So, where do we start? Well, the goal here is to isolate x and find its value. This reminds me of a treasure hunt where each clue leads you closer to your treasure. Here’s the first clue in this mathematical quest: we need to eliminate every distraction from the equation. In this case, we can get rid of that pesky -3 by adding 3 to both sides.

Hold on, let’s clarify that a bit. When you do an operation on one side of an equation, you must also do it on the other side to keep things balanced—just like a seesaw!

Starting with our equation: [4x - 3 = 9] Add 3 to both sides: [4x = 12]

Now, we’ve made some progress! But we’re still not quite at our treasure yet. The next step is to divide both sides by 4. Why? Because we want to solve for x, not 4x!

So, let’s divide:

[x = \frac{12}{4}] Which simplifies to: [x = 3]

But hang on a second! We're not done yet; we need to double-check our options. If you recall, our choices were:

• A. -6
• B. -3
• C. 3
• D. 6

Perfect! Option C, which gives us x = 3, is indeed our calculated answer. But just to be thorough, let’s examine the other options.

Option A (-6)? If we plug it back into the equation, we’d have (4 \cdot -6 - 3 = -27), definitely not our original equation.

Option B (-3)? Let’s see: (4 \cdot -3 - 3 = -15) — no way that fits either.

And what about Option D (6)? Plugging it in gives us (4 \cdot 6 - 3 = 21).

Now, here’s the catch: along the way, we stumbled upon a common misconception. Many might see 3 in our answer and jump back to pick D, thinking they made an error when in truth, the original calculation stands firm, reminding us that it’s all about clarity in solving.

You might wonder, “What’s the main takeaway here?” It’s quite simple, really. Always double-check your work and your chosen answers! Practice makes perfect, and the more equations you unravel, the more confident you’ll feel tackling the next one.

Locking down the nature of equations, like 4x - 3 = 9, is a beneficial skill set. It’s not just for acing tests or CLEP exams; it's like building your toolbelt for real-life problem-solving situations, from budgeting to even planning that next big purchase. Who knew algebra could come in handy beyond the classroom, right?

So keep practicing these principles, question your answers, and don’t shy away from those equations! With each challenge conquered, you’re one step closer to mastering college algebra and getting that passing score on the CLEP. Happy calculating!