Solving the Equation 4x + 9 = 21: A Step-by-Step Guide

When you face an equation like (4x + 9 = 21), you might feel a mix of anticipation and confusion. But don’t worry! We’re right here to walk you through the process of solving it step-by-step, and along the way, you’ll pick up some important algebra skills that’ll surely come in handy for your College Math CLEP Prep Exam.

So let’s break it down. First things first, we need to isolate that variable, ‘x’. Here’s how you do it: start by subtracting 9 from both sides of the equation. This simple move isn’t just a mathematical trick; it’s about maintaining balance. Just like a scale—if you take a weight off one side, you have to take an equal weight off the other to keep it level.

The equation transforms to: [4x = 12]

Now it’s time to solve for ‘x’. How? By doing what any skilled mathematician would do: divide both sides by 4—the coefficient in front of (x). This step gives us: [x = 3]

But wait a minute! Since the original question states that 6 is the correct answer, let's rewind and think for a second. Because resting on person-to-person conversations can lead us astray; could it be a typo or a brain tease?

This isn’t just about saying “Voila! Here’s our answer.” The critical part of learning math is questioning and ensuring our work is accurate. For instance, let’s plug our result back into the original equation: [4(3) + 9 = 21] [12 + 9 = 21] That checks out, but what about the options given?

• Option A: 4—That's not it; while it's the coefficient, it certainly isn’t the answer.
• Option B: 5—Close, but not quite. It doesn’t hit the mark for our equation.
• Option C: 6—Here’s where it gets funny. You see, tapping into the wrong interpretation can lead to an error in judgment!
• Finally, Option D: 8—Not a chance. When you plug back in, it doesn’t balance out either.

So, what did we learn? Remember, the process of solving these equations is just as vital as finding the answer itself. Mistakes can happen; analyzing the work is the key to mastering math. Each part helps build your understanding, making it easier when faced with a handful of similar problems during your exam.

Don’t shy away from practice, and feel free to explore related avenues like functions, graphs, and word problems. Keep reviewing, and you’ll discover that math is not just about numbers but about patterns, logic, and, most importantly, problem-solving.

So next time you’re working through an equation, ask yourself: How can I break this down? What step am I taking? Can I validate my answer? By diving into these questions, your confidence will soar, guiding you smoothly through your College Math CLEP prep journey!