Simplifying Expressions: A Guide for the ACT Aspire Mathematics Test

When it comes to preparing for the Mathematics ACT Aspire Test, mastering simplification of expressions is essential. You know what? Many students find this part a bit tricky, but once you get the hang of it, it can actually be a breeze. Let’s breakdown how to simplify an expression step by step.

Take this expression as an example: ( 5(x + 2) - 3(x - 4) ). To tackle it, we start by distributing the constants across the terms in parentheses. Seems simple enough, right? But let’s walk through it together.

First, distribute the ( 5 ) in ( 5(x + 2) ). Crank that out and you’ll get: [ 5(x) + 5(2) = 5x + 10 ] Pretty straightforward!

Now for the second part: distributing the ( -3 ) in the term ( -3(x - 4) ). Here’s how that breaks down: [ -3(x) + -3(-4) = -3x + 12 ] So far, we’ve gathered ( 5x + 10 ) and ( -3x + 12 ). Now, let’s combine these results: [ 5x + 10 - 3x + 12 ]

What do we have now? Time to combine like terms—one of the most important math skills! Start with the ( x ) terms:

• ( 5x - 3x ) gives us ( 2x ).

And don’t forget about the constant terms: [ 10 + 12 = 22 ]

Putting it all together, we find that the simplified form becomes: [ 2x + 22 ] It’s easy to see how things can get misinterpreted, especially with answer choices like ( 2x + 26 ). It’s vital to track each step closely and verify your work.

Now, you might wonder, why is this so important? Well, the ACT Aspire isn’t just about getting the right answer; it’s about showing your process and understanding the how and why behind it. Think of it like cooking: if you follow the recipe step by step, you won’t just make a meal—you’ll know how to tweak it to your taste.

In addition to your skill building, remember to tackle practice problems regularly. The more you practice, the more confident you’ll feel. Looking for additional resources? There are plenty of study guides and online tools out there that can help you hone your skills.

Whether you're facing the ACT Aspire soon or just brushing up on your algebra skills, remember that every problem helps solidify your understanding. After all, math is just like a puzzle, and with each piece, you get closer to completing the whole picture! Good luck, and keep practicing!