Simplifying Algebraic Equations Like a Pro

What is a solution to the equation c + (4 - 3c) - 2 = 0?

• A. -2
• B. 1
• C. -1
• D. 0

Answer: (C)

To find a solution to the equation c + (4 - 3c) - 2 = 0, we start by simplifying the left side. First, distribute and combine like terms: c + (4 - 3c) - 2 simplifies to c - 3c + 4 - 2. Combining the constant terms (4 - 2) gives us 2, and combining the coefficients of c (c - 3c) gives us -2c. The equation now reads: -2c + 2 = 0. Next, isolate the variable c by moving the constant term to the other side: -2c = -2. To solve for c, divide both sides by -2: c = 1. As per the given options, the correctly simplified and solved version yields c = 1, confirming that this is the solution to the original equation. This demonstrates the first steps in handling simple algebraic equations, focusing on combining like terms and isolating the variable to find its value.

Are you gearing up for the Postsecondary Education Readiness Test (PERT)? If so, mastering algebraic equations is key! Let me share a clearer look at a classic equation: ( c + (4 - 3c) - 2 = 0 ). Sounds a bit daunting at first, right? Don’t sweat it! Let’s walk through it step-by-step.

First things first, you’ve gotta simplify the left side. We start with ( c + (4 - 3c) - 2 ). What do we do here? It's time to combine like terms. Think of it like organizing your closet—getting everything nice and tidy! Distributing and grouping our terms, we get ( c - 3c + 4 - 2 ). Cozy, right?

Now, let's break it down. Combining the constants ( 4 - 2 ) gives us 2, while piecing together the coefficients of ( c ), specifically ( c - 3c ), results in ( -2c ). We’ve now transformed the equation to:

( -2c + 2 = 0 ).

What’s next? Our goal is to isolate that sneaky variable ( c ). Think of it as giving ( c ) some space to breathe. To do that, let's move that constant 2 to the other side. What does that look like? We end up with:

( -2c = -2 ).

To solve for ( c ), we divide both sides by -2. This step’s important because it reveals the value we’re ultimately hunting for. Voilà! We find that ( c = 1 ). Looking back to our choices, does that line up? Sure enough, ( c = 1 ) fits!

Now, you might be thinking, why does this matter? Well, algebra isn't just about numbers; it's about logic and problem-solving! Plus, getting familiar with these steps helps you grasp more complex concepts. That’s the beauty of it!

In conclusion, handling algebraic equations isn't just for classroom settings or tests like PERT; it’s a skill you’ll carry with you. So next time you bump into problems, take a deep breath, and remember the power of simplifying!

Keep practicing, and you’ll find these basic principles become second nature. Who knows? You might even start helping your friends out too! After all, sharing knowledge is one of the most rewarding parts of learning.