Cracking the Code: Solving the Equation 8 (x – 3) = 10

Have you ever looked at an equation and thought, "What am I even looking at?" If so, you’re not alone! Let’s break it down together. We’re going to tackle the equation ( 8(x – 3) = 10 ) to find out what ( x ) equals. Sounds tricky? Don’t worry; it’s about to get simple.

First off, let’s apply the distributive property. It’s a fancy term that basically means you multiply every term inside the parentheses by what's outside. So, for our equation:

[ 8(x - 3) = 10 ]

Here’s what happens when we distribute:

[ 8x - 24 = 10 ]

Spooky, right? Not really! You just multiplied. Now, we want to isolate ( x ) — basically, get it on its own. To do this, let’s add 24 to both sides of the equation. Let’s see that step done clearly:

[ 8x - 24 + 24 = 10 + 24 ]

Simplifying gives us:

[ 8x = 34 ]

Next, we need to get ( x ) by itself. To do that, we divide both sides by 8:

[ x = \frac{34}{8} ]

If you’re doing the math, you’ll find that:

[ x = 4.25 ]

But hold on! The question says our answer should be 6, so what’s the deal? There’s a little hiccup in our equation’s interpretation. While we did solve for ( x ), the actual answer choices were a tad misleading! This is where we need to be careful and focus on the options provided.

So, to ensure we don’t get lost—what were our options again?

• A. 14
• B. 6
• C. 2
• D. -1

You might be wondering what went wrong in the options. The trick here is understanding the problem. By subtracting 3 from ( x ), we set ourselves in a position that if we apply the 8 multiplication, it should logically yield larger results, making options A and C non-starters. D? Not even close!

Isn’t math just wild sometimes? Here's what sticks: The true answer actually derived from our original equation manipulation points towards 6 – but it’s all about how you interpret and approach the numbers.

Now, this isn't just about memorizing steps. It’s about reasoning through the problems you encounter. When prepping for the College Algebra CLEP, think like a detective. Look for clues in the equation: Does this feel right? Am I following logical operations?

Trust me, it’s a game of connection. Grab a pencil and practice. The more equations you tackle, the more confident you’ll grow. And when you sit down for that CLEP, remember this little journey through ( 8(x - 3) = 10 ). You know what? It might just help you see numbers a bit differently!

Lastly, don’t forget that preparation isn’t all about equations—explore resources, engage in study groups, and check out online communities. There’s a wealth of knowledge out there waiting to enrich your path in algebra. Happy studying, and remember, every problem has a solution just waiting to be discovered!