Solve For X: X + 870 + 3659 = 2587

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Solve for x: x + 870 + 3659 = 2587

Hey guys! Today, we're going to dive into solving a simple algebraic equation. Specifically, we need to find the value of 'x' in the equation x + 870 + 3659 = 2587. Don't worry, it's easier than it looks! We'll break it down step-by-step, so you can follow along and understand exactly how to tackle these kinds of problems. Stick with me, and you’ll be a pro in no time!

Understanding the Equation

At its heart, an equation is like a balanced scale. What you do to one side, you must also do to the other to keep it balanced. In our case, we have x + 870 + 3659 = 2587. Our main goal is to isolate 'x' on one side of the equation. This means getting 'x' all by itself, so we know exactly what its value is. To achieve this, we'll use inverse operations. Inverse operations are simply operations that undo each other. For example, addition and subtraction are inverse operations, and so are multiplication and division.

Before we start isolating 'x', let’s simplify the equation a bit. We can combine the numbers on the left side of the equation. So, we'll add 870 and 3659 together:

870 + 3659 = 4529

Now our equation looks like this:

x + 4529 = 2587

This is much simpler to work with, right? Now, we can move on to isolating 'x'.

Isolating 'x'

To isolate 'x', we need to get rid of the '+ 4529' on the left side of the equation. To do this, we'll use the inverse operation of addition, which is subtraction. We'll subtract 4529 from both sides of the equation to keep it balanced. This gives us:

x + 4529 - 4529 = 2587 - 4529

On the left side, +4529 and -4529 cancel each other out, leaving us with just 'x'. On the right side, we need to subtract 4529 from 2587. This will give us a negative number because 2587 is smaller than 4529.

2587 - 4529 = -1942

So, our equation now reads:

x = -1942

And that's it! We've found the value of 'x'. It's equal to -1942. Now, let's move on to the verification step to make sure our answer is correct.

Verifying the Solution

Verifying our solution is a crucial step to ensure we haven't made any mistakes along the way. To do this, we'll substitute the value we found for 'x' back into the original equation. If the equation holds true, then we know our solution is correct.

Our original equation was:

x + 870 + 3659 = 2587

Now, we'll replace 'x' with -1942:

-1942 + 870 + 3659 = 2587

Let's simplify the left side of the equation. First, we'll add 870 and 3659 together:

870 + 3659 = 4529

So now we have:

-1942 + 4529 = 2587

Now, we'll add -1942 to 4529:

-1942 + 4529 = 2587

So, the equation simplifies to:

2587 = 2587

Since both sides of the equation are equal, our solution is correct! x = -1942 is indeed the correct value for 'x' in the equation.

Why Verification Matters

Always remember, guys, verifying your solution is not just an extra step; it's an essential part of the problem-solving process. It helps you catch any errors you might have made while solving the equation. It's like double-checking your work to make sure everything adds up. By verifying, you gain confidence in your answer and ensure that you're on the right track. Think of it as your safety net!

Common Mistakes to Avoid

When solving equations like this, there are a few common mistakes that students often make. One common mistake is forgetting to perform the same operation on both sides of the equation. Remember, the equation is like a balanced scale, and you need to keep it balanced. Another common mistake is making arithmetic errors when adding or subtracting numbers. Always double-check your calculations to avoid these errors.

  • Incorrectly Combining Like Terms: Make sure you are only combining numbers that are constants. For instance, combining 'x' with a constant number would be incorrect.
  • Forgetting the Negative Sign: When subtracting a larger number from a smaller number, the result will be negative. Don't forget to include the negative sign in your answer.
  • Misunderstanding Inverse Operations: Always use the correct inverse operation to isolate 'x'. For example, if 'x' is being added to a number, you need to subtract that number from both sides of the equation.

Practice Makes Perfect

Now that we've solved this equation together, it's time for you to practice on your own. Try solving similar equations with different numbers. The more you practice, the better you'll become at solving algebraic equations. Remember to always show your work and verify your solutions to ensure you're on the right track. Keep practicing, and you'll master these skills in no time!

Real-World Applications

Solving equations like this might seem like just an academic exercise, but it actually has many real-world applications. For example, you might use algebraic equations to solve problems related to finance, such as calculating interest rates or balancing your budget. You might also use them in science to calculate distances, velocities, or forces. Understanding how to solve algebraic equations is a valuable skill that can help you in many different areas of life.

Conclusion

So, there you have it! We've successfully found the value of 'x' in the equation x + 870 + 3659 = 2587, and we've verified our solution. Remember, the key to solving these kinds of problems is to understand the concept of inverse operations and to always keep the equation balanced. With practice, you'll become more confident and skilled at solving algebraic equations. Keep up the great work, and I'll see you in the next lesson! Keep practicing, and you'll be solving equations like a pro in no time. Remember, math is all about practice and understanding the fundamentals. Keep up the great work, and you'll be amazed at what you can achieve!