Here's how to simplify the expression 5(2x + 3) - 4x

Demystifying Algebra: Simplifying Expressions with Ease

Algebra can feel like a cryptic puzzle at times, can’t it? But once you get the hang of it, simplifying expressions becomes a breeze. Let’s tackle a common example that might pop up in your study sessions: simplifying an expression like (5(2x + 3) - 4x). Sounds tricky? Not at all! Let’s break it down step by step.

What's the Big Idea?

Alright, so here’s the expression in question:

[

5(2x + 3) - 4x

]

At first glance, it might seem intimidating, but I promise it’s all about knowing how to dance with the numbers and the letters (or variables, if you want to get technical). First thing's first: the distributive property.

The Power of Distribution

So, what’s this distributive property some folks rave about? It’s a nifty little rule that tells you how to multiply a number outside of parentheses by everything inside them. Think of it as a friendly reminder that you can’t leave anyone out at the party. Here, you’re making sure that (5) gets to mingle with both (2x) and (3).

Let’s apply it to our expression:

[

5 * 2x + 5 * 3

]

Doing the math, you get:

[

10x + 15

]

Nice, right? That wasn’t so bad! But hold tight; we’re not done yet.

Mixing It Up

Now, remember we still have the (-4x) lurking at the end of our equation. We need to toss this guy into the mix. So, let’s combine our new favorite term (10x + 15) with (-4x):

[

10x + 15 - 4x

]

Here comes the fun part—combining like terms! This is just a fancy way of saying we’re adding or subtracting similar terms (those pesky variables with the same letter).

So, (10x - 4x) equals (6x). Quiet applause for our math skills, please!

Now, we can finalize our expression:

[

6x + 15

]

What’s the Answer?

Ta-da! Our simplified expression is (6x + 15). Now, here's where things get a little twisty: if you were looking at answer choices, you might’ve seen:

• A. (x + 15)

• B. (6x + 15) (ding ding ding!)

• C. (10x + 15)

• D. (x + 5)

If you guessed B, pat yourself on the back!

But wait a minute... the original answer provided suggested choice A ( (x + 15) ). Ah, the beauty (and confusion) of algebra!

Why It’s Important

Now, why does this matter? Simplification isn’t just an exercise in math; it’s a skill that lays the groundwork for more complex concepts. Think of it like learning to ride a bike. Balancing on those two wheels is crucial before you tackle those tricky downhill slopes. Having a solid grasp of algebraic manipulation leads to success in tackling equations, inequalities, and even those dreaded word problems.

Real-Life Relevance

You know what’s cool? Algebra isn’t just a classroom thing. It sneaks its way into our daily lives! From cooking recipes where you need to double ingredients to budgeting your next shopping spree—who knew math could be so relatable?

Imagine needing to adjust a recipe that calls for (2x) cups of flour, and you only have a (5(2x + 3)) bag. By keeping your algebra skills sharp, you can adjust those calculations in a flash.

Wrapping It Up

In summary, mastering the steps to simplify expressions like (5(2x + 3) - 4x) is more than just finding a numeric answer; it’s about building confidence and capability in your mathematical journey. So the next time you encounter a similar expression, remember to distribute, combine like terms, and most importantly, have fun with it!

So, what’s next? Dive into more algebraic expressions, maybe tackle some equations, or even challenge yourself with a word problem. But remember, every little step you take in understanding algebra is a step towards unlocking (whoops, sorry!) mastering your math skills. Keep practicing, and you’ll find that it’s not just a series of numbers and letters on a page—it’s a world of possibilities waiting for you to explore!