Mastering College Algebra: Solve for y with Ease

Ever find yourself staring blankly at an algebra equation, feeling like it's written in an alien language? Don't sweat it! Today, we’ll tackle a simple yet fundamental equation to sharpen your skills for the College Algebra CLEP Exam. You know what they say, practice makes perfect, and this lesson is a stepping stone toward mastering college-level algebra.

Let’s dive into our example: solve for y in the equation (3y - 9 = 18). This isn't just any equation; it’s an opportunity for you to polish your algebraic prowess. Let’s break it down step-by-step.

First things first—what does it mean to solve for y? Essentially, we want to isolate the variable y so we can figure out its value. Think of y as a prize hidden behind a locked door, and we need to use the right key to get it open. Our goal here is to perform the opposite operations to untangle y from the equation.

Step 1: Add 9 to Both Sides

To start, we need to eliminate the -9 on the left side of the equation. So, we’ll add 9 to both sides. Here’s the math:

[ 3y - 9 + 9 = 18 + 9 ]

This simplifies to:

[ 3y = 27 ]

Just like that, we've simplified our equation. But hold up, we’re not done yet!

Step 2: Divide by 3

Next, we have to get rid of the 3 that’s multiplying y. To do this, we divide both sides by 3:

[ \frac{3y}{3} = \frac{27}{3} ]

This gives us:

[ y = 9 ]

Oh wait! It looks like we momentarily slipped there. If you catch that, excellent! There's a typo we'll address later; let's return to the original options given. The correct solution leads us to Option C: 9! But why are the other options incorrect?

Let's Talk About the Incorrect Options

Before we move ahead, let’s check the other choices:

• Option A: -3
  Substituting -3 back into the equation: (3(-3) - 9 = -9 - 9 = -18). Not equal to 18, so that’s out!

• Option B: 3
  Now for 3: (3(3) - 9 = 9 - 9 = 0). Again, not equal to 18. We won't be using that option either!

• Option D: 15
  For this one, substituting gives us: (3(15) - 9 = 45 - 9 = 36). Still not equal to 18.

So, as we’ve seen, the only correct option is C: 9!

Wrapping it Up

Isn’t it satisfying to peel back the layers of an equation? The skills you build with practice will not only help you ace the College Algebra CLEP Exam but also lay a solid foundation for any further math courses you might take. Remember, algebra is like a puzzle—you just have to find the right pieces to fit!

The next time you face an equation, don’t panic. Apply the techniques we discussed and watch those algebraic mysteries unravel beautifully. Always remember: it’s not just about finding the answer; it’s about understanding the process. Happy studying!