Mastering Equation Solutions: Why x=9 Matters

Have you ever looked at an equation and thought, “How on earth do I solve this?” You’re not alone! Solving equations can seem like a daunting task at first glance, but with a little practice and the right approach, it becomes as easy as pie. So, let’s tackle a straightforward equation together. We’ll work with the equation (6x - 48 = 6) and find out what (x) is — spoiler alert, it’s not as complicated as you might think!

First things first, we notice that our goal is to isolate the variable (x). In simpler terms, we want to get (x) all by itself on one side of the equation. This is crucial because the clearer our equation is, the easier it is to understand. So here’s what we’ll do: we’ll add 48 to both sides. Why? Because we want to eliminate that pesky -48 hanging out next to our variable. Here’s how that looks:

[
6x - 48 + 48 = 6 + 48
]

This simplifies nicely to:

[
6x = 54
]

Feeling good so far? I hope so! Next, we need to rid ourselves of that coefficient in front of (x) — the 6. To do this, we’ll divide both sides of the equation by 6. Pretend we’re doing a little equation dance; balance is key. So our equation becomes:

[
x = \frac{54}{6}
]

And just like that, you find that:

[
x = 9
]

See! Not so scary after all. But you might be wondering, “What’s the deal with those values I got for (y) and (z) earlier?” Well, when we're solely focused on the value of (x) in this equation, those other variables don’t play a part in our calculations. It’s like they’re just observers, hanging out while we solve the mystery of (x).

To recap, the original equation (6x - 48 = 6) simplifies to (x = 9) after isolating the variable by adding and dividing. This approach is fundamental in algebra, and mastering it sets you up for successes with more complex problems down the line. Who knows? Maybe in the future, you’ll feel like a math magician, pulling out solutions with ease!

So, when preparing for the Accuplacer Test or any other assessments in algebra, remember the dance of isolating variables, practicing not just this equation but many others. The more you practice, the more confident you will become. Trust me; you’ll be ready to tackle those tests with a smile on your face! Let’s keep practicing, because every equation solved is a step closer to math mastery.