Evaluate Expression: -0.4(3x-2) + (2x+4)/3, X=4

Alright guys, let's break down this math problem step by step. We're asked to evaluate the expression $-0.4(3x - 2) + \frac{2x + 4}{3}$ when $x = 4$. This means we need to substitute the value of $x$ into the expression and simplify it to get our final answer. Buckle up, because we're about to dive into some arithmetic!

First, we'll replace every instance of $x$ in the expression with the number 4. This gives us $-0.4(3(4) - 2) + \frac{2(4) + 4}{3}$. Now, following the order of operations (PEMDAS/BODMAS), we need to deal with the parentheses first. Inside the first set of parentheses, we have $3(4) - 2$. Multiplication comes before subtraction, so we calculate $3(4)$ which equals 12. Then, we subtract 2 from 12, which gives us 10. So, the first part of the expression becomes $-0.4(10)$.

Next, let's tackle the fraction. Inside the numerator of the fraction, we have $2(4) + 4$. Again, we multiply first: $2(4)$ equals 8. Then we add 4 to 8, giving us 12. So, the fraction becomes $\frac{12}{3}$. Now our expression looks like this: $-0.4(10) + \frac{12}{3}$. We're getting closer to the solution!

Now, we perform the multiplication and division. $-0.4(10)$ equals -4. And $\frac{12}{3}$ equals 4. So, our expression simplifies to $-4 + 4$. Finally, adding -4 and 4 gives us 0. Therefore, the value of the expression $-0.4(3x - 2) + \frac{2x + 4}{3}$ when $x = 4$ is 0. That wasn't so bad, was it? Remember to take it one step at a time, and always follow the order of operations. And most importantly, double-check your work to avoid those sneaky arithmetic errors! Understanding the step-by-step breakdown ensures that you can tackle similar problems with confidence, solidifying your math skills.

Step-by-Step Breakdown

Let's walk through a more detailed breakdown to make sure every step is crystal clear. This is super helpful for anyone who wants to really understand the nitty-gritty of how we arrived at our answer.

1. Substitute x = 4: We start by replacing every instance of x with 4 in the original expression: $-0.4(3(4) - 2) + \frac{2(4) + 4}{3}$

2. Simplify Inside Parentheses (First Term): Inside the first set of parentheses, we have 3(4) - 2. Following the order of operations, we multiply first: 3 * 4 = 12 Then we subtract 2: 12 - 2 = 10 So the first term becomes -0.4(10).

3. Simplify Inside Parentheses (Second Term - Numerator): In the numerator of the fraction, we have 2(4) + 4. Again, we multiply first: 2 * 4 = 8 Then we add 4: 8 + 4 = 12 So the fraction becomes $\frac{12}{3}$.

4. Perform Multiplication and Division: Now we have -0.4(10) + \frac{12}{3}. Let's do the multiplication and division: -0.4 * 10 = -4 12 / 3 = 4 The expression now looks like -4 + 4.

5. Perform Addition: Finally, we add -4 and 4: -4 + 4 = 0

So, the final answer is 0. Each step is straightforward, but keeping track of the order and the signs is crucial.

Common Mistakes to Avoid

When evaluating expressions like this, it's easy to make small errors that can throw off your entire answer. Here are some common mistakes to watch out for:

• Forgetting the Order of Operations: This is the biggest one! Always remember PEMDAS/BODMAS (Parentheses/Brackets, Exponents/Orders, Multiplication and Division, Addition and Subtraction). Make sure you're performing operations in the correct order.
• Sign Errors: Be extra careful with negative signs. A simple mistake like forgetting a negative sign can completely change the result. Double-check each step to ensure you're handling signs correctly.
• Arithmetic Errors: Even simple addition, subtraction, multiplication, or division errors can lead to the wrong answer. Take your time and double-check your calculations, especially when dealing with decimals or fractions.
• Incorrect Substitution: Make sure you're substituting the value of $x$ correctly into the expression. It's easy to accidentally substitute the wrong number or miss a term.
• Misunderstanding Fractions: When dealing with fractions, remember the rules for adding, subtracting, multiplying, and dividing fractions. Make sure you simplify fractions correctly.

By being aware of these common pitfalls, you can significantly reduce the chances of making mistakes and improve your accuracy when evaluating expressions. Always take a moment to review your work and look for potential errors. Seriously, do it!

Practice Problems

To really master evaluating expressions, it's important to practice, practice, practice! Here are a few more problems you can try on your own:

1. Evaluate $2(x + 3) - 5$ for $x = 2$.
2. Evaluate $\frac{3x - 1}{4} + 0.5x$ for $x = 5$.
3. Evaluate $-1.2(2x - 4) + \frac{x + 2}{2}$ for $x = 3$.

Work through each problem step-by-step, paying close attention to the order of operations and sign conventions. Check your answers carefully, and don't be afraid to ask for help if you get stuck. The more you practice, the more confident you'll become in your ability to evaluate expressions accurately and efficiently. Think of it like leveling up your math skills! Each problem you solve makes you stronger and more prepared for future challenges.

Conclusion

Evaluating expressions is a fundamental skill in mathematics. By understanding the order of operations, being careful with signs, and practicing regularly, you can master this skill and build a solid foundation for more advanced math concepts. Remember to take your time, double-check your work, and don't be afraid to ask for help when you need it. With a little effort and persistence, you'll be evaluating expressions like a pro in no time! Keep up the great work, and never stop learning! You got this!