Mastering Algebra: Solving Linear Equations in Ontario Mathematics

When it comes to algebra, solving equations might seem daunting at first, but it’s really just like piecing together a puzzle. It’s all about isolating that elusive variable, and once you get the hang of it, trust me, it starts to feel like second nature. Let’s tackle a typical question you might find on the Ontario Mathematics Proficiency Test.

So, picture this: you’re faced with the equation ( 5x - 3 = 2x + 6 ). Don’t let it intimidate you! The goal here is to figure out what ( x ) is. Where do we start? Well, we’re going to rearrange the terms seamlessly — think of it as organizing your backpack for school. First things first, let’s get all those ( x ) terms together on one side and the constant terms neatly on the other.

You can start by subtracting ( 2x ) from both sides. This kicks things off nicely:

[ 5x - 2x - 3 = 6 ]

Now, we’re simplifying things. What’s ( 5x - 2x )? That’s right, it’s ( 3x ). Now our equation becomes:

[ 3x - 3 = 6 ]

Here’s where we tidy up even further. Let’s isolate that ( x ) by adding 3 to both sides — no biggie! This gives us:

[ 3x - 3 + 3 = 6 + 3 ]

Now you’ll notice the equation has transformed into:

[ 3x = 9 ]

Excellent! Now, we just need to find what ( x ) equals. It’s not rocket science; simply divide both sides by 3:

[ x = \frac{9}{3} ]

From this calculation, you’ll find:

[ x = 3 ]

And there you have it! The solution to the equation ( 5x - 3 = 2x + 6 ) is 3, which makes option C your correct choice!

Now, why is getting comfortable with these steps crucial before you hit the exam? Imagine going in with the confidence that comes from knowing just how to tackle questions like these, just like a great sports team preparing for a championship. The more you practice these, the more you've got your strategies down pat, making your study time a bit less stressful.

So, that’s a simple yet effective way to approach solving equations for your Ontario Mathematics Proficiency assessment. Remember, practice makes perfect. Make sure you tackle similar problems as you prepare — after all, nothing beats getting hands-on experience!

And hey, if you’re looking for additional resources, don’t forget to check out online practice tests or algebra study guides that can help further sharpen your skills!

So next time you’re faced with an equation, just take a deep breath, trust the process, and piece together that solution like the math champion you are!