Solve For X: X - 5 = -9

Hey guys, let's dive into a classic algebra problem that's super common in mathematics. Today, we're tackling the equation x - 5 = -9. This might look a little intimidating with that negative number in there, but trust me, it's straightforward once you get the hang of it. The main goal here is to isolate 'x', meaning we want to get 'x' all by itself on one side of the equals sign. Think of it like a balancing act; whatever you do to one side, you have to do to the other to keep things equal. So, let's break down how we can achieve that isolation and find the value of 'x' that makes this equation true. We'll explore the steps involved in solving this linear equation, making sure to explain the reasoning behind each move. This type of problem is fundamental to understanding more complex algebraic concepts, so getting a solid grasp on it now will really pay off down the line. We'll also look at the provided options and figure out which one is the correct solution. It's all about understanding the basic principles of equation manipulation. Remember, practice makes perfect, and by working through examples like this, you'll build confidence and skill in no time. Let's get started on finding that elusive 'x'!

Understanding the Equation: x - 5 = -9

Alright, let's really dig into what x - 5 = -9 means in the world of mathematics. At its core, this is a linear equation. That means the highest power of our variable, 'x' in this case, is just 1. We're essentially looking for a specific number that, when you subtract 5 from it, gives you -9. It's like a mystery number puzzle! The equals sign (=) is the key; it tells us that the expression on the left side (x - 5) has the exact same value as the expression on the right side (-9). Our mission, should we choose to accept it, is to uncover the identity of 'x'. To do this, we need to employ some algebraic magic. The most important rule in algebra is maintaining balance. If you were to lift one side of a seesaw, the other side would go up. Similarly, in an equation, if you add, subtract, multiply, or divide a number on one side, you must do the same operation to the other side to keep the equality intact. This principle is what allows us to move terms around and simplify the equation until 'x' stands alone. We'll use inverse operations to undo the operations currently being performed on 'x'. Since 5 is being subtracted from 'x', the inverse operation is addition. By adding 5 to both sides, we'll start peeling away the layers to reveal 'x'. This process isn't just about getting an answer; it's about understanding the logical steps that lead to that answer, a skill that's invaluable not just in math class but in problem-solving in general. So, let's prepare ourselves to apply these fundamental rules to solve for 'x'.

Step-by-Step Solution to x - 5 = -9

Now for the fun part, guys: actually solving x - 5 = -9! Our main objective is to get 'x' by itself. Right now, 'x' has a '- 5' attached to it. To undo the subtraction of 5, we need to perform the opposite operation, which is adding 5. And remember the golden rule of equations? Whatever we do to one side, we must do to the other to keep it balanced. So, we'll add 5 to the left side of the equation:

x - 5 + 5

And because we added 5 to the left, we must add 5 to the right side as well:

-9 + 5

Now, let's simplify both sides. On the left, '- 5 + 5' cancels each other out, leaving us with just 'x'.

x

On the right side, we need to calculate '-9 + 5'. When you add a positive number to a negative number, you're essentially moving closer to zero on the number line. Think of it this way: you owe 9 dollars, and you find 5 dollars. You still owe 4 dollars. So, -9 + 5 equals -4.

-4

Putting it all together, we get:

x = -4

And there you have it! We've successfully isolated 'x' and found its value. The solution to the equation x - 5 = -9 is x = -4. To double-check our work, we can substitute -4 back into the original equation: (-4) - 5 = -9. This is correct! -4 minus 5 does indeed equal -9. This confirmation reinforces that our steps and our final answer are accurate. This method of using inverse operations to isolate the variable is a cornerstone of algebra and applies to a vast array of equations. Keep practicing these basic steps, and you'll master solving for unknowns in no time.

Checking the Answer: Is x = -4 Correct?

It's always a super smart move in mathematics, guys, to check your work. We've just solved x - 5 = -9 and arrived at the answer x = -4. But how do we know for sure that it's the right answer? We do this by substituting our found value of 'x' back into the original equation. This is like plugging in a suspect's name into the crime scene details to see if it fits perfectly. Our original equation is x - 5 = -9. Now, wherever we see 'x', we're going to replace it with '-4'.

So, the equation becomes:

(-4) - 5 = -9

Let's evaluate the left side of this equation: (-4) - 5. Subtracting 5 from -4 means we're moving further down the number line into more negative territory. If you're already at -4 and you subtract another 5, you end up at -9. So, the left side simplifies to:

-9

Now, let's look at the right side of our substituted equation. It's simply:

-9

So, we have:

-9 = -9

Since the left side equals the right side, our solution x = -4 is indeed correct! This verification process is crucial. It not only confirms our answer but also builds our confidence in our algebraic skills. It shows that the logic we applied – using inverse operations to isolate the variable – works flawlessly. This technique of substitution and checking is fundamental, and you should make it a habit whenever you solve an equation. It catches potential errors and solidifies your understanding of how equations function. So, next time you solve a problem, don't forget to do a quick check. It’s a small step that yields big rewards in accuracy and learning.

Analyzing the Multiple-Choice Options

Okay, so we've rigorously solved x - 5 = -9 and confidently determined that x = -4. Now, let's look at the multiple-choice options provided, just to make sure we're aligned and to reinforce why our answer is the standout winner.

The options are:

a) -14 b) -4 c) 4 d) 14

Our calculated solution is x = -4, which directly matches option b. Let's briefly consider why the other options are incorrect. If we were to mistakenly add 5 and 9 together, we might get 14 (option d). If we subtracted 9 from 5 (which isn't what the equation suggests), we might get -4, but the operation is x - 5. If we made a sign error in our addition, perhaps thinking -9 + 5 = -14, that would lead us to option a. Option c, 4, would be the correct answer if the equation was x + 5 = -9 or x - 5 = -1 (a different scenario entirely). The key is that our step-by-step process, which involved adding 5 to both sides of the equation, led us unequivocally to -4. When you perform -9 + 5, you are moving towards zero on the number line, from -9 up by 5 units, landing precisely on -4. The substitution check further solidifies that -4 is the only value for 'x' that satisfies the original equation. So, when faced with multiple-choice questions like this, remember to trust your methodical solution process. Derive the answer first, then find the matching option. This approach minimizes the chance of choosing an incorrect answer based on common errors or guesswork.

Conclusion: The Solved Equation

We've successfully navigated the algebra of x - 5 = -9, guys! By applying the fundamental principle of maintaining balance in equations and using inverse operations, we systematically isolated the variable 'x'. We added 5 to both sides of the equation to undo the subtraction, which resulted in x = -4. Furthermore, we performed a crucial verification step by substituting -4 back into the original equation, confirming that (-4) - 5 indeed equals -9. This confirms our solution is accurate and reliable. The answer -4 corresponds to option b) in the multiple-choice list. Understanding how to solve basic linear equations like this is a foundational skill in mathematics. It’s the building block for tackling more complex problems in algebra and beyond. Keep practicing these steps – identify the operation, apply the inverse operation to both sides, simplify, and always check your answer. With each problem you solve, you'll become more adept and confident in your mathematical abilities. Keep up the great work, and happy solving!