Finding the Value of x in Algebraic Equations

When tackling algebraic equations, especially ones like ( 3(x - 4) = 12 ), it’s helpful to break it down into manageable steps—kind of like solving a puzzle, right? Let’s keep this simple and engaging, focusing on the resolve to get to that elusive value of ( x )!

First up, let’s isolate the variable on one side. You start with ( 3(x - 4) = 12 ). Here’s the thing: our first move is to get rid of that pesky number in front of the parentheses by dividing both sides by 3. This yields:

[ x - 4 = \frac{12}{3} ]

Now, that simplifies cleanly to:

[ x - 4 = 4 ]

Can you almost feel it? The solution is within our grasp! What’s next? Well, to get ( x ) all by itself—like how you clear space for your favorite snack—you add 4 to both sides of the equation:

[ x = 4 + 4 ]

And lo and behold, we get:

[ x = 8 ]

So there we have it—the value of ( x ) is 8. It’s so satisfying to see the math flow lead us directly to the answer, validating every step we took along the way.

Even if you feel a little unsure at points, every methodical step allows you to maintain balance in the equation, reinforcing the beauty of algebra's logical structure. This type of problem-solving not only prepares you for the Mathematics ACT Aspire Test but is also a great exercise in critical thinking—helping to hone your skills beyond just what’s on the test.

Whether you’re prepping for future exams or just brushing up on your mathematical prowess, remember: each equation you encounter is another step toward mastering the subject. Accuracy matters, and with practice, you’ll tackle even the trickiest questions with confidence!