Simplifying $(7x - 2.8) - (3x + 1.2)$ Step-by-Step

Hey guys! Let's dive into simplifying the algebraic expression $(7x - 2.8) - (3x + 1.2)$. This is a common type of problem you'll encounter in algebra, and it's all about combining like terms. Don't worry, it's not as scary as it looks. We'll break it down into easy-to-follow steps, so you'll be a pro at simplifying expressions in no time. This expression involves variables, coefficients, and constants. Our goal is to make it as simple as possible. We need to combine the 'x' terms and the constant terms separately. The key is to carefully distribute the negative sign and then combine similar elements. Alright, let's get started. Remember, practice makes perfect, so don't be afraid to try this problem out a few times until you get the hang of it. You've got this! Let's break down this problem. This guide will walk you through the process, ensuring you understand each step. We'll start with the basics, making sure you're comfortable with the concepts before moving on to the more complex parts.

Step-by-Step Simplification Process

Step 1: Distribute the Negative Sign

First things first, we need to deal with that negative sign in front of the second set of parentheses. Remember, when you have a minus sign outside parentheses, it's like multiplying everything inside the parentheses by -1. So, $(7x - 2.8) - (3x + 1.2)$ becomes $7x - 2.8 - 3x - 1.2$. See how the signs of the terms inside the second set of parentheses have changed? The $+3x$ became $-3x$, and the $+1.2$ became $-1.2$. This distribution step is super important, so make sure you get it right! Always remember, a negative sign in front of a parenthesis changes the sign of each term inside. This step is crucial, and it’s where many people make mistakes. Carefully distributing the negative sign sets us up for success in the next steps. After you've distributed the negative, you should have an expression with no parentheses, which makes it much easier to work with. It's like unwrapping a present; now we can see all the individual components.

Step 2: Identify Like Terms

Now that we've gotten rid of the parentheses, it's time to identify the like terms. Like terms are terms that have the same variable raised to the same power. In our expression, $7x - 2.8 - 3x - 1.2$, the like terms are $7x$ and $-3x$ (because they both have 'x') and $-2.8$ and $-1.2$ (because they are both constants). Identifying like terms is the key to the next step, where we'll actually combine them. Make sure to include the sign in front of each term when you identify its like terms. This ensures you're accounting for whether the term is positive or negative. Correctly identifying the like terms is an essential skill in algebra and will help you solve more complicated equations later on. So, take your time and double-check your work; it's always better to be safe than sorry when it comes to math! Remember, like terms have the same variable and exponent. Constants are also like terms.

Step 3: Combine Like Terms

Time to put it all together! Now that we've identified our like terms, we can combine them. We'll handle the 'x' terms first: $7x - 3x = 4x$. Then we'll deal with the constants: $-2.8 - 1.2 = -4$. So, combining these like terms gives us $4x - 4$. And that, my friends, is our simplified expression! This step is where we actually perform the addition or subtraction of the like terms. When combining, pay close attention to the signs. A positive and negative term will be subtracted, while two negatives will add up to a larger negative. Double-check your arithmetic, especially when dealing with negative numbers. This step is all about making the expression as concise as possible. It is where all the previous work comes to fruition, resulting in a cleaner and more manageable expression. Always simplify your work for clarity.

Step 4: The Final Simplified Expression

After all these steps, the simplified form of $(7x - 2.8) - (3x + 1.2)$ is $4x - 4$. This is the simplest form of the expression because we have combined all like terms. Congratulations, you did it! You've successfully simplified the expression. The final expression $4x - 4$ is a linear expression, and it's much easier to work with than the original expression. Understanding how to simplify expressions like this is fundamental for solving more complex algebraic problems. Now you're ready to tackle more advanced problems. This is the culmination of all the steps. It represents the final and most simplified form of the original expression. The answer is clear and easy to understand. You have successfully reduced a complex expression into its simplest form.

Tips and Tricks for Success

To make sure you're acing these problems every time, here are a few extra tips and tricks:

• Always double-check your work: It's easy to make small mistakes, especially with signs. Go back and review each step. It is very important to make sure everything is perfect.
• Practice makes perfect: The more you practice, the easier it will become. Try different examples. Doing multiple problems will build your confidence.
• Write out each step: Don't try to skip steps, especially when you're starting out. This helps you avoid making errors.
• Pay attention to signs: Seriously, this is a big one. A misplaced negative sign can change everything! Always be careful with the signs.
• Break it down: If you're feeling overwhelmed, break the problem down into smaller parts. Tackle one step at a time.
• Use a calculator (but understand the process): Calculators can be helpful for arithmetic, but make sure you understand the underlying concepts. They can help but always know how to do it by yourself.
• Ask for help: Don't be afraid to ask your teacher, classmates, or a tutor if you're stuck. It’s okay to need help, we all need help sometimes.

Why Simplifying Expressions Matters

Simplifying expressions is a fundamental skill in algebra and mathematics in general. It's not just about doing well on tests; it's a foundation for understanding more complex concepts. Here's why it's important:

• Solving Equations: Simplifying expressions is a crucial step in solving algebraic equations. By simplifying, you can isolate the variable and find its value. It makes it easier to figure out what the variables mean.
• Problem-Solving: Math problems often involve complex expressions. Simplifying helps you break down problems into manageable parts.
• Building a Foundation: A solid understanding of simplifying expressions prepares you for advanced topics like calculus, physics, and engineering. It builds a base for bigger and better things.
• Real-World Applications: Simplification is used in various fields, from finance to computer science. You use it in many different careers.
• Efficiency: Simplified expressions are easier to work with. They reduce the chance of making errors and save you time. They make life easier.

Common Mistakes to Avoid

Here are some common mistakes people make when simplifying expressions, and how to avoid them:

• Forgetting to distribute the negative sign: This is the most common mistake. Make sure you change the sign of every term inside the parentheses. Distributing the negative is a must.
• Combining unlike terms: Only combine terms with the same variable and exponent. You can't combine $x$ and a constant. Keep them separate.
• Making arithmetic errors: Double-check your addition, subtraction, multiplication, and division. Use a calculator if needed, but make sure you understand the process. Always double-check your arithmetic.
• Forgetting the coefficient: Don't forget the number in front of the variable (the coefficient). It's important. The coefficient matters.
• Not simplifying completely: Make sure you've combined all like terms and written the expression in its simplest form. Leave no stone unturned.

Conclusion: Mastering Expression Simplification

So there you have it, guys! We've successfully simplified the expression $(7x - 2.8) - (3x + 1.2)$. By following these steps and tips, you should be well on your way to mastering the art of simplifying algebraic expressions. Remember to practice regularly, pay attention to detail, and don't be afraid to ask for help when you need it. Simplifying expressions is a fundamental skill that will serve you well in all areas of mathematics. Keep practicing, and you'll get better and better. This process, while seemingly simple, is a crucial skill for more advanced concepts. Now go out there and conquer those algebraic expressions! You're ready to tackle more complex math problems and become a math whiz. Congrats again on finishing, and keep up the great work. Keep practicing and keep learning! You’ve got the tools you need to succeed in algebra and beyond. Keep up the excellent work, and never stop learning!