Getting to Grips with Algebra: Solving for x in Equations

Getting to Grips with Algebra: Solving for x in Equations

When staring at an equation like 3(2x - 4) = 21, you may feel a mix of confusion and determination. But don’t worry! We're breaking it down step by step, so you can tackle algebra with confidence. Ready? Let’s solve for x!

Distributing with Style

First things first, we need to distribute that 3 on the left side. It’s like giving the equation a little nudge, right? So, let’s distribute:

[ 3(2x) - 3(4) = 21 ]
That simplifies to: [ 6x - 12 = 21 ]

At this point, you might be thinking, "Wait, is this straightforward enough?" Absolutely! It’s all about taking it one step at a time.

Isolate the x

Next up, we want to isolate that elusive x. You might think of it like pulling your favorite sweater out of a messy closet—it’s there, just hidden. So, we’ll add 12 to both sides to simplify things:

[ 6x - 12 + 12 = 21 + 12 ]
Which gives us: [ 6x = 33 ]
Now we’re getting closer! You can practically feel the excitement!

Final Steps to Freedom

To solve for x, we just need to divide both sides by 6. It’s kind of like splitting a pizza into equal slices—you want a fair share:

[ x = \frac{33}{6} ]
This gives us: [ x = 5.5 ]

An Unexpected Twist

Now, here’s where it gets interesting. You might have noticed that the options given were integers:

• A. x = 4
• B. x = 5
• C. x = 7
• D. x = 10

Since our calculation results in 5.5, and doesn’t exactly match option B (which states x = 5), it’s understandable to feel a little perplexed. How do we navigate this?

While it’s easy to assume that the integer option would likely be the preference, mathematics thrives on exactness—5.5 is indeed the correct solution! So what if none of the given options match? Well, it's a reminder that sometimes math tests can be tricky!

A Learning Experience

Mistakes happen, and this discrepancy is a prime example of why checking your calculations is crucial. If ever you encounter such issues, take a moment to believe in your process. Sometimes, despite the confusion, it can enhance understanding and prepare you for similar situations in the future.

Mathematical Confidence is Key!

So, how do you prepare for what lies ahead in your college math placement test? Practicing similar algebraic equations is essential. Familiarizing yourself with various problems helps build confidence and reinforces the skills you need.

You know what? Math becomes easier with practice! And with every solved equation, you're not just answering questions; you’re building a toolkit of skills that will carry you through college and beyond.

Remember, when faced with equations, think of them as puzzles waiting to be solved. With patience and practice, you'll tackle them head-on! And who knows, you might end up solving them faster than you think.