Mastering College Algebra: Simplifying Expressions with Ease

What is the simplified form of the expression 4x + (4x + 8) + (2x + 6)?

• A. 14x
• B. 10x
• C. 6x
• D. 8x

Answer: (A)

In this expression, we have multiple terms with the variable x. To simplify the expression, we need to combine like terms, or terms with the same variable. The first and second terms, 4x and 4x, can be combined to give 8x. Similarly, the third and fourth terms, 2x and 6, can be combined to give 8. So, the full expression becomes 8x + 8 + 8, which can be further simplified to 16x + 8. The simplified form of this expression is 16x + 8, which is equivalently written as (8 * 2x) + 8. Therefore, the correct simplified form is equivalent to having a total of 2x + 8, or 14x, which is option A. The other options, B, C, and D,

Have you ever felt overwhelmed seen an algebra expression like (4x + (4x + 8) + (2x + 6)? Yeah, it can seem daunting at first glance. But breaking it down? That’s where the magic happens! Let’s step through this together, shall we?

Getting Started: Trust the Process

First things first, let’s simplify this expression by combining like terms. Imagine you’re assembling a puzzle – and the pieces that fit together hold the most value. Since we have several terms featuring (x), our goal is to group them and find our answer. Here’s the expression again:

[

4x + (4x + 8) + (2x + 6)

]

You might be thinking, “Where do I even begin?” Well, let’s tackle the (4x) terms while we’re at it. So, (4x + 4x) works its magic to give us (8x). Pretty neat, right? Now we’re looking at:

[

8x + (2x + 8 + 6)

]

Combining Like Terms: The Key to Simplification

Now, check this out! The (2x) adds in nicely with our (8x). So you add (2x) to (8x), and boom! You’ve got (10x). But hold on! We still have those constants hanging out in the parentheses.

Now, let’s combine the numbers inside the parentheses – (8 + 6). Do the math, and that equals (14), right? We definitely want that in our final answer! Toss it in with our (10x):

[

10x + 14

]

Now we’re getting somewhere! But our expression still needs a little polish. What else can we do? It’s all about presenting our findings in an elegant way.

The Grand Finale: The Simplified Expression

Let’s simplify the expression a little further. The expression now is (10x + 14). Don’t worry if you feel like you’ve seen it all before. Every algebra problem has its unique twist.

Now, if you were to factor this expression, you might notice there’s a common factor of (2) between (10x) and (14). Divide both terms by (2) and guess what you get?

[

= 2(5x + 7)

]

Feels great, doesn’t it? But we’re still on a quest to find the earlier mishap! In our original analysis I misstepped slightly; our answer isn’t (14x); instead, it’s a beautiful (10x + 14).

Takeaways: Prepare for the CLEP Exam

So, why are we focusing on this tricky little expression? The College Algebra CLEP Prep exam is a challenge for many students, and yes, simplifying expressions is one of its favored topics. It’s like training for a big game; you need to practice the plays beforehand!

Understanding how to combine like terms with confidence is a great strategy. On exam day, you’ll face not just expressions, but also word problems and other algebra concepts that will be calling upon your skills.

So, keep practicing. Work through problems like (4x + (4x + 8) + (2x + 6)) until it feels second nature. And if you hit a wall? Just remember: breaking down the problem is half the battle. You got this!

Remember, algebra doesn’t have to be scary, and with consistent practice, you’ll tackle that CLEP exam like a boss. Ready, set, simplify!