Solving Math Equations: Find The Value Of X

Hey guys! Today, we're diving into a fun little math problem that combines two different operations. It looks a bit complex at first, but don't worry, we'll break it down step by step. Our mission is to find the value of 'x' that makes everything balance out perfectly. So, grab your thinking caps, and let's get started!

Understanding the Operations

Before we jump into solving the equation, let's make sure we understand what these operations actually mean. We have two operations here:

1. The first operation, which looks like ×|: This operation takes a number 'x', multiplies it by 3, and then subtracts 3. So, if we have ×|, it means 3x - 3.
2. **The second operation, which looks like **: This operation takes a number 'x', adds 1 to it, and then multiplies the whole thing by 2. So, if we have , it means 2(x + 1).

It's super important to get these definitions clear in our heads before we move on. Once we know what these symbols do, the rest is just algebra. Think of it like a little code we need to decipher! Make sure to understand the underlying principles of these operations. Without grasping these concepts, you might find yourself lost in the maze of algebraic manipulations. Always start by ensuring you have a solid understanding of the fundamental definitions. Remember, math is all about building on a solid foundation!

Now, let's try a quick example to make sure we're on the same page. Suppose x = 5. Then ×| would be 3 * 5 - 3 = 12. And `` would be 2 * (5 + 1) = 12. See? Once you get the hang of it, it's not so scary. Keep practicing, and you'll become a pro in no time! Understanding these operations isn't just about solving this specific problem; it's about building a toolkit of mathematical skills that you can use in all sorts of situations. So, take your time, ask questions, and enjoy the process of learning. Math is an adventure, and you're the explorer!

Setting Up the Equation

Okay, now that we know what our operations mean, let's look at the equation we need to solve:

2 ×| =

This equation tells us that applying the first operation to the number 2, and then applying the second operation to that result, should give us the same thing as applying the second operation directly to 'x'. Sounds complicated? Let's break it down!

First, let's apply the ×| operation to 2. That means we substitute 2 for 'x' in the expression 3x - 3:

×| = 3 * 2 - 3 = 6 - 3 = 3

So, ×| equals 3. Now we need to apply the `` operation to this result. That means we substitute 3 for 'x' in the expression 2(x + 1):

= 2 * (3 + 1) = 2 * 4 = 8

So, the left side of our equation, 2 ×|, simplifies to 8. Now we can rewrite our original equation as:

8 =

This is much simpler! We've taken the complicated original equation and boiled it down to something we can actually work with. The key here was to take it one step at a time. Don't try to do everything at once! Break the problem down into smaller, manageable chunks. It's like eating an elephant – you can't do it in one bite! Each operation is a bite-sized piece that you can easily handle. And once you've chewed through all the pieces, you've solved the whole problem! Remember, patience and persistence are your best friends in math. Keep chipping away at the problem, and you'll eventually reach the solution. And don't be afraid to ask for help along the way. We're all in this together!

Solving for x

Alright, we're in the home stretch now! We've simplified our equation to:

8 =

And we know that `` means 2(x + 1). So, we can rewrite the equation as:

8 = 2(x + 1)

Now it's just a matter of using our algebra skills to isolate 'x'. First, we can divide both sides of the equation by 2:

8 / 2 = 2(x + 1) / 2

4 = x + 1

Next, we subtract 1 from both sides:

4 - 1 = x + 1 - 1

3 = x

So, we've found that x = 3! That's it! We've solved the equation. Give yourself a pat on the back. You've earned it!

Remember, the key to solving these kinds of problems is to stay organized and take it one step at a time. Don't try to rush things, or you're more likely to make mistakes. And always double-check your work to make sure you haven't made any silly errors. Math is like a puzzle, and each step is a piece of the puzzle. Once you put all the pieces together correctly, you get the big picture. And the feeling of accomplishment is totally worth it! So, keep practicing, keep learning, and keep having fun with math!

Checking Our Answer

Before we declare victory, let's make absolutely sure our answer is correct. It's always a good idea to plug our solution back into the original equation to verify that it works.

Our original equation was:

2 ×| =

And we found that x = 3. So, let's substitute 3 for 'x' in the right side of the equation:

= 2 * (3 + 1) = 2 * 4 = 8

Now let's check the left side. We already know that 2 ×| simplifies to 8, so the left side is also 8.

Since both sides of the equation are equal when x = 3, we can confidently say that our answer is correct!

See? Checking your work is super important! It's like proofreading a paper before you turn it in. You might catch a mistake that you didn't see before. And it gives you peace of mind knowing that you've done everything correctly. So, always take the extra few minutes to check your answer. It's worth it!

And that's a wrap, folks! We've successfully solved for x in our combined operation equation. Hope you had fun, and more importantly, hope you learned something new. Keep practicing, and you'll become a math whiz in no time! Remember to always break down complex problems into smaller, manageable steps, understand the fundamental definitions, and double-check your work. Happy solving!