Finding Solutions to Algebraic Equations Made Easy

Getting the hang of algebra can feel like a daunting task at first. But fear not! Once you break down the steps, it becomes clearer—and maybe even fun. Today, we’re taking a closer look at how to find the solution for the equation -6x = 48. This is essential knowledge for anyone tackling the College Algebra CLEP Prep, and it might just spark your enthusiasm for math.

So, what’s the first thing we need to do? Well, let’s isolate x on one side of the equation. To solve -6x = 48, we need to get rid of that pesky -6 in front of our variable x. You know what? The simplest way to do this is by dividing both sides of the equation by -6. It’s like balancing a scale; whatever you do to one side, you must do to the other to keep everything fair and square.

Here’s how it shakes out: [ x = \frac{48}{-6} ] Once you simplify that, you’ll find that: [ x = -8 ] Oops! But wait, hold that thought. It looks like I slipped there; let’s ensure we’re on the right track for the problem we started with, which is finding the correct solution to the original equation.

Now, looking at our possible answers: -2, -8, 8, and 2; we can see that –8 is a potential answer based on our calculation. However, let’s double-check these choices against our equation to ensure we have the right solution.

Moving on from our mistake, let's try the other numbers. What happens if we test -2? When you substitute it into the equation, you get: [ -6(-2) = 12 ] Hmm, not quite correct. Now let’s check -8: [ -6(-8) = 48 ] Bingo! So while it seems like we were set on -8, this is not the only way to check if one of our choices works.

But let’s clarify—what our goal here is to find is the correct correlation between the multiplication of x and -6 leading to the answer being equal to 48, which keeps leading us back to 8 as a potential valid answer.

Every time you multiply back:

• For -2, which gives -12 (not a fit),
• For -8, you get, well, 48!
• And what about 2? It turns the equation around nicely, making it another option.

So after all that fact-checking and digging deeper through the numbers, let's conclude with a recap. The correct answer to “What is the solution of -6x = 48?” is indeed -8!

But here’s where it gets tricky. In your upcoming College Algebra CLEP preparation, ensure each possible answer is truly tested against the requirements of the equation. It’s not just about solving; it’s validating your answers that brings that knowledge home.

Finding solutions to algebraic equations like this one doesn't just serve as pen-and-paper homework. It strengthens analytical skills and teaches you how to navigate through the web of numbers, preparing you for tests and real-world applications alike. Remember: math isn't just about numbers; it’s about clarity and logic!

So, as you're getting ready for your upcoming exam, remember to keep these strategies in your toolbox. Practice, validate, and watch your algebra skills soar. Good luck!