Mastering College Algebra: Your Guide to Solving Equations Like a Pro

Ever feel like algebra is a language all its own? You're definitely not alone! Many students face challenges when tackling problems like the one above: 3(x - 2) = -27. But don’t worry; let’s break this down together.

Ready to Solve? Let’s Get Started!

To tackle this equation, we want to use the distributive property. This sounds fancy, but essentially, it just means distributing a number across those parentheses. So, we start by multiplying 3 by both terms in the parentheses (x and -2). Here’s how it looks:

3(x - 2) = -27 becomes 3x - 6 = -27.

Pretty neat, right? Now, it becomes a bit more manageable. The next step is isolating x, and who doesn’t love finding “x”?

Adding a Little to Both Sides

Now, let’s get that pesky -6 out of the way. To do this, we’ll add 6 to both sides of the equation. So it looks like this:

3x - 6 + 6 = -27 + 6, simplifying to 3x = -21.

Bingo! We’re closer to our goal.

Divide and Conquer

The final stretch involves dividing both sides by 3 to solve for x:

3x / 3 = -21 / 3, leading to x = -7.

And there you have it! The solution to the equation 3(x - 2) = -27 is x = -7—definitively not any of the other options!

What About Those Other Choices?

You might be wondering about the other options: A. 5, B. -3, and D. 3. Here’s the lowdown on why they don’t work:

• Option A: 5
  Plugging in 5 gives: 3(5 - 2) = 3 * 3 = 9, which clearly doesn’t equal -27.

• Option B: -3
  Now, substituting -3, we have 3(-3 - 2) = 3 * -5 = -15—not equal to -27.

• Option D: 3
  And for 3, we get 3(3 - 2) = 3 * 1 = 3—not equal to -27 either!

Practice Makes Perfect

Now that you've mastered this particular equation, remember—it’s all about practice. The more you work with algebraic equations, the easier they’ll become. Don’t shy away from getting stuck; that’s part of the learning curve. Who knows, the next time you face a challenge, you’ll breeze through it like a pro!

Also, keep in mind that using different resources, from online problem solvers to study groups, can give you the extra edge you need. Everybody learns differently, so keep trying different methods until you find what clicks for you.

So, as you gear up for that College Algebra CLEP exam, remember: the key is understanding the process. Break down those equations, take it step by step, and don’t forget to celebrate small victories along the way!

Keep shining, future algebra whiz!