How to Find the Value of x in an Algebra Equation

Finding the Value of X: A Casual Guide to Algebra

So, you've stumbled upon a classic algebra problem—finding the value of ( x ) in the equation ( 6x - 3 = 3x + 9 ). It's one of those straightforward tasks that seems daunting at first, but hang tight; it’s all about breaking it down step by step. Let’s dive into the sweet world of solving algebraic equations together. You ready? Let’s go!

What’s the Goal Here?

First off, what we're really trying to do is isolate ( x ). Think of ( x ) as that intriguing mystery guest at a party. You just want to get to know them better, right? But to do so, we need to clear out some of the noise—basically, those pesky numbers and terms that are hanging around.

In algebra, this means moving everything around until ( x ) is sitting pretty on one side of the equation all by itself. So, how do we get there? Let’s take a closer look.

Step 1: Rearranging the Equation

We start with our equation:

[

6x - 3 = 3x + 9

]

It can be a bit like trying to untangle a set of headphones—sometimes, you just have to start pulling at the straps. First, let’s move all the terms that include ( x ) to one side and the constant terms to the other side.

Here’s how to do it: subtract ( 3x ) from both sides. It’s like clearing out the clutter:

[

6x - 3x - 3 = 9

]

Now, that transforms our equation a bit:

[

3x - 3 = 9

]

Feel that? We’re getting closer to that little elusive ( x ).

Step 2: Tackling the Constants

Next up, we’ve got to deal with the constant on the left side. But how? Simple! We add 3 to both sides. Think of it as adding another piece to our puzzle:

[

3x - 3 + 3 = 9 + 3

]

And voilà! We’ve simplified that side:

[

3x = 12

]

See how things are beginning to clear up? We're almost there!

Step 3: The Final Countdown

Now, to truly isolate ( x ), we can’t forget to divide both sides by 3. It’s like a gentle nudge to remind ( x ) that it’s ready to be all on its own:

[

x = \frac{12}{3} = 4

]

And there we go! We’ve found our prize: ( x = 4 ).

Before we move on, doesn’t it feel satisfying to solve an equation like this? It’s like completing a jigsaw puzzle or finally remembering where you left your car keys.

So, What Does This All Mean?

When you substitute ( x = 4 ) back into our original equation, it checks out perfectly:

[

6(4) - 3 = 3(4) + 9

]

Breaking that down gives:

[

24 - 3 = 12 + 9

]

Which is:

[

21 = 21

]

And there you have it: the equation holds true. You’ve effectively danced through the steps of algebra like a pro—how cool is that?!

A Little Extra: The Real-World Connections

You know, algebra isn’t just some dry, academic exercise—it’s actually everywhere! From budgeting your monthly expenses to understanding how much paint you need for a DIY project, those numbers and variables come into play. Ever tried to calculate a discount while shopping? That’s some real-world algebra right there!

Conclusion: Embracing the Challenge

So, the next time you see an equation that seems like a mountain to climb, remember our quick and friendly steps to isolate ( x ). It’s all about breaking it down and not getting overwhelmed by the mountain of numbers. Remember, every algebra problem is like a little puzzle waiting to be solved, and with practice, you’ll find yourself tackling them with confidence.

Don’t shy away from the challenge—instead, embrace it! So, what’s next? More equations, perhaps? Whatever you choose, take it step by step, and you’ll find that things start to click. Happy solving!