Mastering College Algebra: A Simple Breakdown of Operations

When it comes to tackling complex math problems, particularly in College Algebra, one vital concept stands out: the order of operations. If you're gearing up for the College Algebra CLEP Prep, getting comfortable with this idea can be a game-changer. So, let’s break it down using a seemingly simple question to illustrate: What is the value of (12 + 5 - 3) × 2?

Getting Started: The Equation

Alright, here’s a quick rundown of that equation: (12 + 5 - 3) × 2. You’ve got a bunch of numbers hanging out together, and they’re just waiting to be solved. But before you jump in, there’s a crucial rule to remember: the order of operations. You’re probably familiar with PEMDAS—it's like your secret navigation tool through the math jungle!

Deciphering PEMDAS

Okay, let’s unpack PEMDAS! This stands for Parentheses, Exponents, Multiplication/Division, and Addition/Subtraction. It’s the hierarchy of operations that keeps your answers in check. If you follow it, you’ll avoid common pitfalls that lead to mistakes.

Step 1: Solve Inside the Parentheses

So, the first step tells us to address what’s inside the parentheses. Here, you’d first do (12 + 5 - 3). Doing that math, we find:

[ 12 + 5 - 3 = 14 ]

Step 2: Multiply the Result

Now you take that result, 14, and multiply it by 2:

[ 14 × 2 = 28 ]

Wait—28? But, if your options were A. 98, B. 100, C. 106, and D. 144, you've got a puzzler here. So let’s figure out where that answer went astray.

Analyzing Incorrect Choices

• Option A (98): This shows a common mistake. If you simply added 12 + 5 + 3 and then multiplied by 2, you’d get a wrong answer of 40. Nope, not even close!

• Option C (106): This answer reveals a mix-up in addition. Perhaps someone just didn’t follow the order correctly.

• Option D (144): Again, this option neglects the subtraction involved in the parentheses and leads to another incorrect conclusion.

So, what's the final answer? It's glaringly clear that the only plausible and correct answer from a strictly algebraic perspective isn’t one of those given options.

Realization: Understanding the Mistakes

Here’s the kicker—you need that order of operations to guide you! When you’re faced with choices in a test, remember: clarity of process will often lead you back to the right answer. Don't forget, each math problem can feel like a mini puzzle. Sometimes, just knowing where the pieces fit can save you from a wrong turn.

Practice Makes Perfect

If you’re prepping for the College Algebra CLEP exam, it’s crucial to hone this skill. Work through practice problems routinely. Not only will this solidify the order of operations in your mind, but it’ll also get you accustomed to the types of questions you might encounter. Think about it: the more you practice, the more instinctive this will become!

Wrapping It Up

So, what’s our take-home message here? Master the basics—embrace PEMDAS like your trusty compass. It’ll guide you through even the trickiest of equations. And as you prep for that College Algebra CLEP exam, just remember: clear thinking and systematic problem-solving can turn those seemingly daunting algebra problems into manageable tasks. Now, go tackle those algebra concepts with confidence!