Mastering the Accuplacer: A Guide to Solving Equations with Confidence

Solve the equation 50 - x - (3x + 2) = 0 when x=3, y=-4, and z=2, what is the outcome?

• A. 1
• B. 8
• C. 12
• D. 15

Answer: (C)

When solving this equation, it is important to use the correct order of operations. In this case, we first need to simplify the expression inside the parentheses by distributing the negative sign, giving us 50 - x - 3x - 2 = 0. Next, we can combine like terms by adding the constants together and the coefficients of x together. This gives us 48 - 4x = 0. From here, we can solve for x by dividing both sides by -4, giving us x = 12. Therefore, the outcome of this equation when x=3, y=-4, and z=2 is 12. Option A is incorrect because it is the solution if we only consider the first part of the equation, 50 - x. Option B is incorrect because it is the solution if we consider the second part of the equation, 3x + 2. Option D is incorrect because it is the result if we add all three values of x, y, and z together instead of solving the equation.

When it comes to preparing for the Accuplacer test, knowing how to solve equations is crucial. Ever found yourself wrestling with an equation that seems like it’s more trouble than it’s worth? You’re not alone! Let’s break down a typical equation you might encounter, doing it step-by-step to build your confidence.

Imagine dealing with the equation: 50 - x - (3x + 2) = 0. Now, if you’re thinking, “Sure, I’ve seen worse!” you’re on the right track. First things first, we must simplify this expression. This is where the order of operations, or PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) comes in handy. You know that feeling when you just nail a puzzle? That’s the goal here!

So, we start off by distributing that pesky negative sign in front of the parentheses. That gives us 50 - x - 3x - 2 = 0. Let’s tidy it up: we can combine like terms for a clearer picture. Keep your eye on the prize: 50 - 2 = 48 and -x - 3x = -4x. Now the equation looks like this: 48 - 4x = 0.

But wait, what happens next? To find x, we’ll isolate it. Seems straightforward enough, doesn’t it? We divide both sides by -4. Voila! x = 12. Now, that wasn’t so scary, was it?

The outcome here is significant because knowing how to methodically tackle equations like these can make a world of difference for your Accuplacer performance.

But let’s bust a myth, shall we? If we simply plug in the values x = 3, y = -4, and z = 2 we don't get 12—better to keep those values for different problems where direct substitution applies. Options A and B may look tempting, but they don’t fit quite right, and it’s essential to know why! Always remember, understanding the process is what truly helps when the pressure's on.

Feeling more at ease? Good! That’s the power of practice. Working out equations can reshape your approach to math altogether, making tricky problems less daunting. Think of it as training for a marathon. The more you practice, the stronger you get!

When studying for the Accuplacer, you’ll want to apply these strategies across various problems. Whether it’s algebra, reading comprehension, or numerical skills, familiarity reduces anxiety. Plus, it feels great when you see your progress over time. Keep pushing through, and remember: every problem solved is a step closer to achieving your goals!