Mastering College Algebra: Solving for x Made Easy

When you're taking on the challenge of the College Algebra CLEP exam, understanding how to solve equations is a must. So, let's break it down with a simple example: Find the value of x in the equation 6x - 7 = 11. Don’t worry if this sounds a bit overwhelming right now; we’ll tackle it together—step by step.

First, you might be thinking, “Where do I even start?” The key here is to isolate the variable x, which means getting x all by itself on one side of the equation. Let’s take that initial equation, 6x - 7 = 11, and add 7 to both sides. Why do we add 7? To eliminate the -7 on the left side, of course! So we have:

[ 6x - 7 + 7 = 11 + 7 ]

This simplifies to 6x = 18. Simple enough, right?

Here’s the thing: now we have 6x all set up, and we need to find x. This is where division comes into play. By dividing both sides by 6, we find:

[ x = \frac{18}{6} ]

And voilà! x = 3. If we look at our options—A. 2, B. 3 (which we just found), C. 4, and D. 5—we can confidently say that option B is the correct answer and the value of x is indeed 3.

Now, let’s unpack why the other choices are incorrect. Starting with option A, which is 2. If we substitute 2 back into the equation, we get:

[ 6(2) - 7 = 12 - 7 = 5 ]

Clearly, not equal to 11. So option A doesn’t fit.

Moving on to option C, if we plug in 4:

[ 6(4) - 7 = 24 - 7 = 17 ]

Again, no match to 11.

And lastly, for option D, substituting 5 gives us:

[ 6(5) - 7 = 30 - 7 = 23 ]

Still isn’t equal to 11. So, you see, with a little work, we verified that 3 is not only the right answer, but the only viable option.

But why does this matter? Mastering such equations in your College Algebra studies helps build the foundation for more complex math concepts down the line. Think of it as laying bricks: the stronger your base, the more resilient your structure will be. You might even encounter variations of this problem throughout your studies, so having solid strategies in place can help you soar.

Remember, practice makes perfect! Grab some more equations and give them a whirl—whether they’re simple like the one we just tackled or a bit more complex. You’ll find each time you work through an equation, you’re not just solving for x; you’re building your confidence and skills for future challenges.

So the next time you’re standing in front of an equation, remember the steps: isolate x, eliminate, solve. And keep that positive mindset; you can conquer College Algebra!