Mastering the Expression: Understanding \( 3(x + 2) + 4 \)

When it comes to tackling algebra, mastering expressions can feel like a daunting task. But guess what? It doesn’t have to be! Let’s explore how to simplify the expression ( 3(x + 2) + 4 ) in a way that makes it all come together, just like a perfectly baked pie—sweet and satisfying!

So, you’re probably thinking, “What’s the first step?” Well, let’s break it down. We've got ( 3(x + 2) + 4 ), and our mission is to make this simpler. It sounds complicated at first, but trust me, it’s easier than pie! First, we need to distribute that pesky 3 to both terms inside the parentheses. Here’s how it works:

[ 3 \cdot x + 3 \cdot 2 + 4 ]

Can you see it taking shape? When we multiply, it turns into:

[ 3x + 6 + 4 ]

Now, I know what you’re thinking: “Okay, but what now?” Here’s the thing—this is where it gets exciting! We’ve got two terms that can be combined—( 6 ) and ( 4 ). So, let’s add those together:

[ 3x + (6 + 4) ]

That gives us:

[ 3x + 10 ]

And voilà! The once complex expression is now simplified to ( 3x + 10 ). So, in our original options, we can confidently say the correct answer is indeed B: ( 3x + 10 ).

But why is this important? Understanding distribution and combining like terms isn’t just an academic exercise—it’s a crucial skill that pops up all over math, especially when preparing for the Ontario Mathematics Proficiency Test. You’ll see variations of this type of problem, and mastering this can pave the way for smoother sailing through more complex problems.

By taking it step by step—much like how you’d approach your favorite recipe—you’re building your mathematical toolkit. Remember, every time you simplify an expression, you're sharpening your math skills. And who doesn’t want to feel that awesome rush of solving a problem?

So as you prepare for your test, keep this simplification method handy. With each expression you tackle, you're not just learning—you're gearing up to face those math challenges with newfound confidence. Now, go on and simplify your way through math like the pro you are!