Solving (1 - 6x) * 3: A Simple Guide

Hey guys, let's dive into how to solve the equation (1 - 6x) * 3. This is a fundamental concept in algebra, and understanding how to approach it can really boost your math skills. We're going to break it down step by step, making it super easy to grasp. Don't worry, it's not as scary as it might look at first glance. By the end of this guide, you'll be able to confidently tackle similar problems. We'll cover the basics, explain the logic, and show you some helpful tricks along the way. Ready to get started? Let's do this!

Understanding the Basics: Order of Operations

Alright, before we jump into the equation itself, let's quickly recap the order of operations. This is super important because it dictates the sequence in which we solve mathematical expressions. Remember PEMDAS or BODMAS? They're basically the same thing, just with different names. PEMDAS stands for:

• Parentheses (or Brackets)
• Exponents (or Orders)
• Multiplication and Division (from left to right)
• Addition and Subtraction (from left to right)

So, when we see an equation like (1 - 6x) * 3, we first need to address what's inside the parentheses. Then, we'll move on to the multiplication. This is the golden rule, and if you get this step right, you're already halfway there! Understanding the order of operations is key to avoiding common mistakes and ensuring you solve the equation correctly. Without following the correct order, you might end up with a completely wrong answer. Think of it like a recipe: if you don't follow the steps in order, your dish might not turn out right. Same idea here, but with math! Keeping PEMDAS in mind will be your best friend throughout this process.

This order ensures everyone solves math problems the same way, leading to consistency and clarity in mathematical communication. Imagine if everyone followed their own rules – it would be chaos! Learning this order isn't just about solving one equation; it's a foundational skill that will serve you well in all areas of mathematics. It helps us to simplify complex expressions systematically and accurately. Each operation builds upon the previous one, and if one step is incorrect, it can mess up everything that follows. So, yeah, remember PEMDAS! It's essential for anyone learning math, and it might be the most crucial concept you will get familiar with!

Step-by-Step Solution: Breaking It Down

Okay, now that we've refreshed our memory on the order of operations, let's tackle the equation (1 - 6x) * 3. Our goal is to simplify this expression. Here's how we'll do it, step by step:

1. Distribute the 3: This means we multiply the 3 by each term inside the parentheses. So, we multiply 3 by 1 and 3 by -6x.
   • 3 * 1 = 3
   • 3 * (-6x) = -18x
2. Rewrite the Equation: Now that we've distributed the 3, the equation becomes: 3 - 18x.

And that's it! We've simplified the expression. There's no more solving we can do here unless we know the value of x. The expression 3 - 18x is the simplified form of (1 - 6x) * 3.

Let's break it down further to make sure everything is crystal clear. The distribution step is the core of this simplification. Basically, we're taking that outside number (3 in this case) and sharing it with everything inside the parentheses. Think of it like this: you have 3 bags of candy, and each bag contains 1 piece of candy and 6 chocolates. To know the total candy and chocolates, you'd multiply both the candy and chocolates by 3. It is the same process here: each term must be multiplied by the value outside the parentheses. Don't forget the signs! If a term has a negative sign, make sure to multiply the outside value to the negative term. This is often a common mistake, so be extra careful. Once you've distributed correctly, the rest is just rewriting the simplified form of the equation. Easy, right?

Example Problems

Let's try some examples to cement our understanding:

1. (2 - 4x) * 5:
   • Distribute the 5: (5 * 2) - (5 * 4x)
   • Simplify: 10 - 20x
2. (-3 + 2x) * 2:
   • Distribute the 2: (2 * -3) + (2 * 2x)
   • Simplify: -6 + 4x

See? It's the same process every time. Just remember to distribute and then simplify. These examples show you the pattern: multiply the number outside the parentheses by each term inside. The negative signs can throw you off sometimes, so always double-check your work. Also, pay attention to how we distribute through the positive and negative signs inside the parentheses. This ensures the answer is correct.

Practice these steps until you feel comfortable with them. The more you practice, the easier it becomes. These are examples, but the same logic applies to any expression of this form. Each time you solve a problem, try to visualize each step in your head. The visualization can aid in the understanding, making it simpler to avoid errors. So, take your time, go through the steps methodically, and with consistent effort, you'll become a pro at this!

Common Mistakes and How to Avoid Them

Even the best of us make mistakes! Here are a few common ones and how to dodge them:

• Forgetting to distribute to both terms: This is the most common error. Always make sure you multiply the number outside the parentheses by every term inside.
• Incorrectly handling negative signs: Be very careful with negative signs. Remember that a negative times a positive is a negative, and a negative times a negative is a positive. Double-check the signs throughout the calculation.
• Adding or subtracting before distributing: Always follow PEMDAS. Multiplication and division come before addition and subtraction. First, deal with the distribution and after that, the addition or subtraction.

Avoiding these mistakes is all about being careful and taking your time. Write down each step, and don't try to do too much in your head at once. Go slowly, especially when you're starting out. Use these tips to catch those potential errors. Review your work carefully, and if something doesn't seem right, don't hesitate to go back and double-check. Practice helps in recognizing these mistakes and fixing them automatically. When you are confident, you will avoid such issues.

Tips for Success

Here are some tips to make your learning experience smooth and effective:

• Practice regularly: The more you practice, the more comfortable you'll become with these types of problems. Do as many exercises as you can. Math is like a muscle - the more you use it, the stronger it gets!
• Break down complex problems: If you encounter a problem that seems overwhelming, break it down into smaller, more manageable steps. This makes it easier to understand and solve.
• Check your work: Always check your answers. If possible, try solving the problem in a different way to verify your solution. This will also help you to spot any errors.
• Don't be afraid to ask for help: If you're struggling with a concept, don't hesitate to ask your teacher, a friend, or a family member for help. There's no shame in seeking help; it's a great way to learn!

Remember, learning math is a journey, not a race. Everyone learns at their own pace, so be patient with yourself. If you struggle, just keep trying. Eventually, you'll be confident with every problem. By staying consistent, practicing and learning, you will do well.

Conclusion: You've Got This!

So, there you have it! We've covered how to simplify the expression (1 - 6x) * 3. Remember the key takeaways:

• Follow the order of operations (PEMDAS).
• Distribute the number outside the parentheses to each term inside.
• Be careful with signs.
• Practice, practice, practice!

You've got this, guys! With a little practice, you'll be solving these types of equations in no time. Keep practicing, stay focused, and you'll be amazed at how quickly you improve. The more you practice, the more confident you will become. Remember that the fundamentals are key in these types of problems, so always double check your work. And most of all, have fun with it! Math can be challenging, but it can also be rewarding and enjoyable. So, keep practicing and keep learning, and you'll go far!