Isolating Variables: Subtracting In 6-2x = -3

by ADMIN 46 views

Hey guys! Let's dive into some algebra today and tackle the question of isolating variables in an equation. Specifically, we're going to break down the equation 6 - 2x = -3 and figure out which number we need to subtract from both sides to get that variable term all by itself. It might sound a bit intimidating, but don't worry, we'll take it step by step and make sure it all clicks. Understanding how to isolate variables is a fundamental skill in algebra, so mastering this concept will really set you up for success in more advanced math. So, grab your pencils, and let's get started!

Understanding the Subtraction Property of Equality

Before we jump into the specific problem, let's quickly recap the subtraction property of equality. This property is a cornerstone of algebraic manipulation, and it basically states that if you subtract the same number from both sides of an equation, the equation remains balanced. Think of it like a seesaw: if both sides are equal, and you take the same weight off each side, the seesaw will still be balanced. In mathematical terms, if a = b, then a - c = b - c. This simple yet powerful rule allows us to manipulate equations to isolate the variable we're trying to solve for. Without this property, solving equations would be incredibly difficult, if not impossible! The subtraction property ensures that whatever operation we perform maintains the equation's integrity, leading us closer to the solution. Therefore, the subtraction property is important.

Analyzing the Equation: 6 - 2x = -3

Okay, let's bring our attention back to the equation at hand: 6 - 2x = -3. Our goal here is to isolate the term with the variable, which in this case is -2x. To do that, we need to get rid of the other term on the same side of the equation, which is the 6. Remember, we're aiming to get the -2x term by itself on one side. Now, think about what operation is currently being applied to the -2x term. We see that 6 is being added to the -2x term (or you can think of it as a positive 6). To undo addition, we need to use its inverse operation, which is subtraction. So, the key here is to figure out what number we need to subtract from both sides to cancel out that 6. Once we understand this crucial step, the rest will fall into place, and we'll be one step closer to solving for x.

Identifying the Number to Subtract

So, we know we need to subtract a number from both sides of the equation to isolate the -2x term. The question is, what number should it be? Looking at the left side of the equation, we have 6 - 2x. We want to eliminate the 6, so it makes sense that we need to subtract 6. If we subtract 6 from 6, we get zero, effectively canceling it out. Remember, though, that we must subtract the same number from both sides of the equation to maintain balance, thanks to the subtraction property of equality. So, we'll be subtracting 6 from both the left side (6 - 2x) and the right side (-3). This ensures that the equation remains true and that we're on the right track to solving for x. This step is critical because choosing the wrong number to subtract would lead us down the wrong path and make it harder to isolate the variable.

Applying the Subtraction

Alright, we've identified that we need to subtract 6 from both sides of the equation. Let's do it! Starting with our original equation, 6 - 2x = -3, we subtract 6 from both sides. This gives us: 6 - 2x - 6 = -3 - 6. Now, let's simplify each side. On the left side, the 6 and -6 cancel each other out, leaving us with -2x. On the right side, -3 - 6 equals -9. So, our equation now looks like this: -2x = -9. See how the -2x term is now isolated on the left side? We've successfully used the subtraction property of equality to move closer to solving for x. This step highlights the power of using inverse operations to simplify equations and isolate variables. We are making progress.

Why Other Options Are Incorrect

Let's quickly address why the other answer choices in the original question are incorrect. This will help solidify our understanding of the process.

  • A. -3: Subtracting -3 would be the same as adding 3. While this is a valid operation, it wouldn't help us isolate the -2x term. It would actually move us further away from our goal.
  • B. -2: Subtracting -2 (or adding 2) also wouldn't eliminate the 6. It might be tempting to think of the -2 because it's the coefficient of x, but we're not trying to isolate x just yet; we're isolating the entire -2x term.
  • C. 3: Subtracting 3 wouldn't directly cancel out the 6 either. It would change the constant term on the left side, but it wouldn't isolate the variable term.

Only subtracting 6 directly eliminates the 6 on the left side of the equation, making it the correct choice. Understanding why the wrong answers are wrong is just as important as knowing why the right answer is right! This type of analysis helps strengthen your problem-solving skills.

Final Answer and Next Steps

So, the correct answer is D. 6. We should subtract 6 from both sides of the equation 6 - 2x = -3 to isolate the variable term. Awesome job, guys! You've successfully navigated this algebraic hurdle. Now that we've isolated the -2x term, the next step would be to divide both sides by -2 to finally solve for x. But that's a lesson for another time! The key takeaway here is understanding how to use the subtraction property of equality to manipulate equations and get closer to your solution. Keep practicing these skills, and you'll become a true algebra whiz. Remember, math is like a muscle – the more you exercise it, the stronger it gets!