Finding the Value of x in Algebraic Equations

What is the value of x in the equation 3(x - 4) = 12?

• A. x = 4
• B. x = 8
• C. x = 6
• D. x = 12

Answer: (B)

To solve the equation \( 3(x - 4) = 12 \), start by isolating the term involving \( x \). First, divide both sides of the equation by 3 to eliminate the coefficient: \[ x - 4 = \frac{12}{3} \] This simplifies to: \[ x - 4 = 4 \] Next, to solve for \( x \), add 4 to both sides of the equation: \[ x = 4 + 4 \] This results in: \[ x = 8 \] Thus, the value of \( x \) is 8, confirming that the correct answer aligns with the solution process. It's important to consider that, while isolating the variable, each step must maintain the equality of the equation, ensuring the correct manipulation of both sides. Therefore, the reasoning leads directly from the original equation through logical steps, validating the correct answer.

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!