Solving (x+7y-4z)+(-12x+3y+10z): A Math Problem

Hey guys! Let's dive into solving this math problem together. We've got an expression that looks a bit like a jumble of letters and numbers, but don't worry, it's easier than it looks. Our mission is to simplify (x+7y-4z)+(-12x+3y+10z). Basically, we need to combine like terms. Think of it like sorting your socks – you put all the same colors together, right? We’re doing the same thing here, but with ‘x’s, ‘y’s, and ‘z’s.

Breaking Down the Expression

First, let's rewrite the expression without the extra parentheses. This makes it easier to see what we're working with:

x + 7y - 4z - 12x + 3y + 10z

Now, let's group the like terms. I'm gonna highlight them so you can easily follow along:

x + 7y - 4z - 12x + 3y + 10z

See how I've grouped the x terms, the y terms, and the z terms? This is a crucial step to avoid mixing things up. Think of it as lining up your ingredients before you start cooking – keeps things organized and efficient.

Combining the 'x' Terms

Alright, let's start with the x terms. We have x and -12x. When we combine them, we get:

1x - 12x = -11x

So, the combined x term is -11x. Easy peasy, right? This is like saying you have one apple, and then you lose twelve apples. You're now eleven apples short!

Combining the 'y' Terms

Next up are the y terms. We have 7y and 3y. Adding these together gives us:

7y + 3y = 10y

So, the combined y term is 10y. Imagine you have seven bananas and you get three more. Now you have ten bananas!

Combining the 'z' Terms

Finally, let's tackle the z terms. We have -4z and 10z. Combining these, we get:

-4z + 10z = 6z

So, the combined z term is 6z. Think of it as owing four cookies but then finding ten cookies. You eat four to pay off your debt, and you’re left with six cookies!

The Final Result

Now that we've combined all the like terms, let's put it all together. We have:

-11x + 10y + 6z

And that, my friends, is our final simplified expression! We took a seemingly complicated expression and broke it down into smaller, manageable parts. Remember, the key is to identify and combine like terms. It's like organizing your closet – once everything is in its place, it's much easier to find what you need.

Practice Makes Perfect

If you're still feeling a bit unsure, don't worry! Practice makes perfect. Try tackling similar problems, and you'll become a pro in no time. The more you practice, the easier it becomes to spot those like terms and combine them correctly. It's like learning to ride a bike – at first, it feels wobbly, but with enough practice, you'll be cruising along smoothly.

Additional Tips for Success

• Double-Check Your Work: Always double-check your work to make sure you haven't made any silly mistakes. It's easy to accidentally drop a negative sign or miscombine terms.
• Write Neatly: Writing neatly can help you avoid confusion and make it easier to spot errors. Trust me, messy handwriting can be a real headache when you're trying to solve math problems.
• Use Different Colors: Use different colors to highlight like terms. This can be especially helpful when you're first starting out.
• Take Breaks: If you're feeling frustrated, take a break. Sometimes, stepping away from a problem for a few minutes can help you clear your head and come back with a fresh perspective.

Real-World Applications

You might be wondering, "When am I ever going to use this in real life?" Well, believe it or not, simplifying expressions like this is actually quite useful in various fields. For example, engineers use it to design structures and circuits, economists use it to model financial markets, and computer scientists use it to write algorithms. So, even though it might seem abstract, this skill can open doors to many exciting opportunities.

Example in Engineering

Imagine you're an engineer designing a bridge. You need to calculate the total load on the bridge, which depends on various factors such as the weight of the materials, the number of vehicles, and the wind speed. These factors can be represented as variables in an expression, and simplifying the expression can help you determine the maximum load the bridge can handle.

Example in Economics

Suppose you're an economist studying the supply and demand of a particular product. You can use expressions to model the relationship between the price of the product and the quantity demanded and supplied. Simplifying these expressions can help you predict how changes in price will affect the market.

Example in Computer Science

Let's say you're a computer scientist writing an algorithm to sort a list of numbers. You can use expressions to represent the steps involved in the algorithm. Simplifying these expressions can help you optimize the algorithm and make it run faster.

Conclusion

So, there you have it! We've successfully simplified the expression (x+7y-4z)+(-12x+3y+10z) to -11x + 10y + 6z. Remember, math is all about breaking down complex problems into smaller, more manageable steps. Keep practicing, and you'll become a math whiz in no time!

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