Mastering Algebra: Simplifying Expressions Step by Step

What is 3(x + 2) + 4(x - 5) simplified?

• A. 3x + 6 + 4x - 20
• B. 7x - 14
• C. 7x + 14
• D. 7x - 6

Answer: (B)

To simplify the expression 3(x + 2) + 4(x - 5), start by distributing the coefficients through each parenthesis. First, multiply 3 by each term in the first parenthesis: 3(x + 2) = 3x + 6. Next, multiply 4 by each term in the second parenthesis: 4(x - 5) = 4x - 20. Now, you can combine the results of these distributions: 3(x + 2) + 4(x - 5) becomes: 3x + 6 + 4x - 20. Next, combine like terms. First, add the coefficients of x: 3x + 4x = 7x. Then, combine the constant terms: 6 - 20 = -14. Putting it all together gives you: 7x - 14. Thus, the correct simplification of the expression is 7x - 14, making it the accurate answer. This clearly shows the step-by-step process of distributing, combining like terms, and organizing the expression correctly to arrive at the simplest form.

Let's break down the world of algebra together! Ever stared at a complex expression, feeling a little lost? You’re definitely not alone. Simplifying algebraic expressions, such as 3(x + 2) + 4(x - 5), can seem daunting at first. The good news? With a bit of practice, it becomes second nature. Ready to tackle it? Let’s go step by step.

Step One: Distributing Coefficients

Here’s the deal: you start by distributing the coefficients across the terms in the parentheses. For our expression, you’ll multiply 3 by each term in the first parenthesis (x + 2):

3(x + 2) becomes 3x + 6. Pretty straightforward, right? Same goes for the second part:

4(x - 5) turns into 4x - 20.

So, if we compile our results, it’s looking like this:

3x + 6 + 4x - 20.

Step Two: Combining Like Terms

Now, onto the fun part—combining like terms! This step is key. First, you simply add the coefficients of x together:

3x + 4x gives you 7x. Quick question: how many times have you skipped straight to the numbers, forgetting about the partners in crime, the constants?

Speaking of constants, let’s tackle those as well. You’ll bring together 6 - 20, which equals -14.

And just like that, we conclude our simplification with 7x - 14! Doesn’t seem too hard when you break it down, does it?

Why This Matters

Now you might be wondering, why does this process even matter? Well, mastering these skills is foundational. Algebra isn’t just about crunching numbers; it’s also about solving real-world problems. Imagine needing to calculate the dimensions of a garden space or understanding your budget—it’s the same algebraic principles guiding you!

While we’ve just looked at one expression, the beauty of algebra lies in its patterns. Each problem you solve brings you closer to a greater understanding and builds your confidence. Plus, the satisfaction you feel when you correctly simplify an expression? Pure gold.

So as you prepare for assessments, including practice tests, remember that each algebraic expression is an opportunity to flex your critical thinking skills. Take your time. Practice will only sharpen your skills further!

Further Resources

If you’re looking to deepen your understanding even more, there’s a treasure trove of online resources available. Websites like Khan Academy or numerous YouTube tutorials provide excellent explanations and practice problems for every learning style.

So, ready to tackle the next expression? You’ve got this! And if you ever feel stuck, just remember: simplify it one step at a time—you only need to distribute, combine, and you’ll find your answer waiting patiently at the end.