How to Effectively Solve the Equation 3(x - 2) = 12

Getting Started with Equations: Mastering the Distributive Property

Let's face it: math can be as puzzling as a jigsaw puzzle with missing pieces. You might find yourself staring at equations, scratching your head and wondering, “Where do I even begin?” If you’ve ever grappled with equations like (3(x - 2) = 12), you’re not alone. But don’t sweat it! Today, we’re diving into the first step to unraveling that problem, and trust me, once you've got this down, you'll feel like a math wizard.

So, What’s the Deal with That Equation?

Alright, let’s break it down. The equation we’re working with is (3(x - 2) = 12). This is where the fun begins. Now, the first thing that pops in when we see an equation like this is to jump right into isolating (x). But hold on a second; there’s an important step we shouldn’t skip.

The Magical Distributive Property

You know what? The key here is to understand the distributive property. It sounds fancy, but it really just means that when you’re multiplying a single term by expressions in parentheses, you need to distribute that multiplier to each part of the expression. In simpler terms, it’s like sharing cookies – if you have three cookies to give to two friends, you’d give one to each friend before deciding who gets the third cookie, right?

So, applying this to our equation, we need to distribute the (3) across the (x - 2). Here’s what we do:

[

3(x - 2) = 12

]

This becomes:

[

3 \cdot x - 3 \cdot 2 = 12

]

Which simplifies to:

[

3x - 6 = 12

]

Now, doesn’t that look a bit more manageable? Distributing that (3) clears up the parentheses and allows us to move on to the next steps without feeling overwhelmed by what’s inside.

Why It Matters

But why does this first step even matter? Well, think of it like decluttering your room. Before you can decide how to organize your space, you need to clear out everything that’s making it messy. Once you do that, it’s much easier to see what you have and figure out where everything should go.

In the case of our equation, clearing out the parentheses allows us to focus solely on the (x) terms. After we distribute, we have a clear path to isolate (x) in the next steps. And just for the record, isolating (x) is usually the ultimate goal in solving equations, but let’s save that for later.

Let’s Move On!

Once we have (3x - 6 = 12), what do we do next? This is where our old friend algebra steps in, guiding us with familiar steps to get (x) all by itself. Here’s the sequence:

1. Add (6) to both sides. What’s the opposite of subtracting (6)? You guessed it! Adding it will get us closer to isolating (x):

[

3x - 6 + 6 = 12 + 6

]

Which gives us:

[

3x = 18

]

2. Divide both sides by (3) to solve for (x):

[

x = \frac{18}{3} = 6

]

And just like that – poof – we’ve determined that (x = 6)!

Connecting the Dots

Now, isn’t it interesting how one simple step can set the stage for the entire problem? The distributive property isn’t just a mathematical principle; it’s a life lesson in breaking down tasks to see the big picture. Whether you’re facing convoluted math equations or organizing your thoughts for a project, take that first step to distribute, or in life terms, to simplify.

Final Thoughts: Embrace the Process

Here’s the thing: don’t shy away from math just because it seems daunting. Understanding the basics, like the distributive property, can give you the confidence to tackle more complex problems. Remember, every monumental achievement starts with a single step – or in this case, a single distribution!

You can do this. Armed with knowledge and a dash of tenacity, math problems like (3(x - 2) = 12) will transform from mind-boggling puzzles into manageable challenges. So go ahead, embrace the process, and who knows? You might just find yourself loving math more than you thought possible!