Mastering the Basics: Solving the Equation 2x + 3 = 7

Let’s take a moment to delve into an essential algebra problem: solving the equation 2x + 3 = 7. This fundamental concept can ease much frustration in your journey toward acing the College Algebra CLEP exam. Whether you’re feeling a little lost or you just want a refresher, let’s simplify it together, shall we?

Now, when we face an equation like this, our goal is to isolate the variable—getting x all by itself on one side of the equation. You might think of it like cleaning up a messy room; we want everything in its right place! So here’s how we do this:

Step one: subtract 3 from both sides. Just like politely asking a friend to step aside to make some room. We take our original equation, 2x + 3 = 7, and transform it as follows:

[ 2x + 3 - 3 = 7 - 3 ]

This simplifies down to:

[ 2x = 4 ]

See how we made progress already? Now, we can move on to the second step: dividing both sides by 2. Again, think of it as sharing the goodies equally among two friends:

[ \frac{2x}{2} = \frac{4}{2} ]

This boils down to x = 2. And voilà! We've found our solution.

But wait—let’s just double-check ourselves, because nothing beats a good critique, right? We have several answer choices here: A. -2, B. -1, C. 1, D. 2. Now, plug in those numbers one by one into the original equation to verify their validity.

• If we try A: -2: [ 2(-2) + 3 = -4 + 3 = -1 \quad→ \quad \text{not equal to } 7. ]

• What about B: -1? [ 2(-1) + 3 = -2 + 3 = 1 \quad→ \quad \text{not equal to } 7. ]

• Let’s check C: 1. [ 2(1) + 3 = 2 + 3 = 5 \quad→ \quad \text{not equal to } 7. ]

• Finally, option D: 2. [ 2(2) + 3 = 4 + 3 = 7 \quad→ \quad \text{yes! this one works.} ]

So, through our little dive into the numbers, we’ve found that D (2) truly holds up under scrutiny as the only correct answer.

This approach might lock in those basic skills you’ll need for the math challenges ahead in your College Algebra journey. As you prepare for the CLEP exam, remember that mastering these kinds of problems will build your confidence. Get accustomed to manipulating equations, and they’ll become second nature, like riding a bike.

Now, here’s the thing: Algebra can sometimes feel like a puzzle, right? But each piece you put together adds clarity to the bigger picture. Keep practicing these concepts, and soon you'll find that algebra isn’t just a series of equations—it’s a language of its own. So, what are you waiting for? Grab your calculator, review these steps, and let’s get back to the books!