Solving Inequalities: A Step-by-Step Guide to Mastering College Algebra

When solving the inequality 5x + 3 > 10, what is the value of x?

• A. 2
• B. 3
• C. 4
• D. 5

Answer: (A)

To solve this inequality, we need to get x by itself on one side of the inequality. To do this, we first subtract 3 from both sides to get 5x > 7. Then, we divide both sides by 5 to isolate x. This gives us x > 1.4, which means that any value of x greater than 1.4 would make the inequality true. Therefore, the value of x can be any number greater than 1.4, including 2, which is the only option greater than 1.4. Options B, C, and D are all less than 1.4 and would not make the inequality true.

When you're preparing for the College Algebra CLEP exam, understanding how to handle inequalities is essential. If you've ever found yourself staring at a problem that says something like 5x + 3 > 10, you probably felt a mixture of curiosity and a bit of dread. But don't worry! By the end of this article, you're going to tackle that inequality like a pro.

So, how do we solve 5x + 3 > 10? Let's break it down step by step, and soon enough, you’ll be raising your hand confidently in class.

Step 1: Getting x Alone

First things first, we've got to isolate x. This is like trying to find that last cookie in a jar—it's all about getting past the other stuff in the way. So, let's subtract 3 from both sides. This gives us:

5x > 7

Now we’re on the right track!

Step 2: Divide and Conquer

Next, it's time to divide both sides by 5. Why? Because we want to see what x is really worth. So:

x > 1.4

This is where the magic happens. X can be any value greater than 1.4. It’s like a number party—all the values greater than 1.4 are invited!

What’s the Answer?

So let's look closely at our choices:

• A. 2

• B. 3

• C. 4

• D. 5

Only option A, 2, is greater than 1.4. B, C, and D don't make the cut; they’re still too cozy with 1.4. So, our answer is clear; x can be 2 or any number above it!

Why Do We Care?

You might be wondering: Why is understanding inequalities so crucial for the CLEP exam (and life in general)? Inequalities pop up everywhere—whether you’re budgeting for the week, planning a project, or even negotiating that dream job. Being able to solve them builds a strong foundation.

Potentials of being wrong? Sure, we all make mistakes; that's how we learn. Still, practice makes perfect, so don’t shy away from trying a few more examples. The more you confront these problems, the more confident you'll become, and that’s a win for anyone.

Final Thoughts

As you tap into this understanding of inequalities, remember: it’s not just about finding the answer; it’s about mastering the process. Don't hesitate to backtrack and remember that practice is key when it comes to algebra. So give yourself a little leeway; engage with various problems, tackle one at a time, and before you know it, you’ll be breezing through the CLEP exam like you own it!

It’s all within your grasp, so keep pushing forward and happy studying!