Triple X Minus 7 Plus 1/5 X: Math Problem Solved!

Hey guys! Today, we're diving into a fun little math problem that might seem tricky at first, but trust me, it's totally solvable. We're tackling the question: What is triple of x minus 7 plus one-fifth of x? Sounds like a mouthful, right? But we're going to break it down step-by-step, so you'll be a pro in no time. So, grab your pencils, and let's get started!

Breaking Down the Problem

First things first, let's translate the words into mathematical expressions. This is like learning a new language, but instead of words, we're using numbers and symbols. Think of it as cracking a code!

• "Triple of x" means 3 times x, which we write as 3x. This is pretty straightforward, right? We're just multiplying x by 3.
• "Minus 7" means we're subtracting 7 from something. In this case, we're subtracting 7 from triple of x, so we get 3x - 7. We're building our expression piece by piece.
• "One-fifth of x" means 1/5 times x, which we can write as (1/5)x or x/5. Fractions might seem scary, but they're just another way of representing a part of a whole.
• "Plus" means we're adding things together. So, we're adding one-fifth of x to what we already have (3x - 7). This is where things start to come together.

Now, let's put it all together. The entire expression becomes: 3x - 7 + (1/5)x. See? It's not as intimidating when we break it down. We've successfully translated the words into a mathematical expression. Now comes the fun part – simplifying it!

Simplifying the Expression

Okay, so we have 3x - 7 + (1/5)x. The goal here is to combine the "like terms." Think of "like terms" as family members – they share something in common. In this case, the terms with 'x' are family, and the numbers without 'x' are another family. We can only combine members of the same family.

So, we have 3x and (1/5)x. These are our 'x' family members. To combine them, we need to add them together. But wait, we're adding a whole number and a fraction. Don't worry, we can handle this!

First, let's convert 3x into a fraction with a denominator of 5. Why 5? Because that's the denominator of our other 'x' term, (1/5)x. To do this, we multiply 3 by 5/5 (which is just 1, so we're not changing the value). So, 3x becomes (15/5)x. Now we're talking the same language!

Now we can add (15/5)x and (1/5)x. When adding fractions with the same denominator, we simply add the numerators (the top numbers). So, (15/5)x + (1/5)x = (16/5)x. We've successfully combined our 'x' family members!

What about the -7? Well, it's the only member of its family (the numbers without 'x'), so it just tags along. It's like the cool loner at the party.

So, our simplified expression is now (16/5)x - 7. We've taken a complicated-looking expression and made it much simpler. We're on a roll!

Understanding the Solution

So, we've simplified the expression to (16/5)x - 7. But what does this actually mean? Well, it's a mathematical expression that represents a relationship between x and another value. If we knew what 'x' was, we could plug it into this expression and get a numerical answer.

For example, let's say x = 5. We can substitute 5 for x in our expression:

(16/5) * 5 - 7

The 5s cancel out, leaving us with:

16 - 7 = 9

So, when x = 5, the value of the expression is 9. Pretty neat, huh?

But what if x was something else? Let's try x = 10:

(16/5) * 10 - 7

This simplifies to:

32 - 7 = 25

So, when x = 10, the value of the expression is 25. You see, the value of the expression changes depending on what 'x' is. This is the beauty of algebra – it allows us to represent relationships between variables.

Why This Matters

Now, you might be thinking, "Okay, this is cool, but why do I need to know this?" Well, understanding how to translate word problems into mathematical expressions and simplify them is a fundamental skill in math and many other fields.

This skill is used in:

• Science: Calculating distances, speeds, forces, and more.
• Engineering: Designing structures, circuits, and machines.
• Finance: Managing budgets, investments, and loans.
• Computer Science: Writing code and developing algorithms.
• Everyday Life: Figuring out the best deals, calculating recipes, and planning trips.

So, mastering these skills opens doors to a whole world of possibilities. Plus, it's just plain satisfying to solve a tricky problem!

Practice Makes Perfect

The best way to get good at this is to practice, practice, practice! Here are a few similar problems you can try:

1. What is twice of x plus 3, minus one-third of x?
2. What is half of x minus 5, plus two times x?
3. What is four times x plus 1, minus one-fourth of x?

Try breaking these problems down into smaller steps, just like we did with the original problem. Translate the words into mathematical expressions, simplify them, and then try plugging in different values for 'x' to see how the expression changes.

Don't be afraid to make mistakes! Mistakes are how we learn. The more you practice, the more comfortable you'll become with these types of problems.

Conclusion

So, guys, we've successfully tackled the question: What is triple of x minus 7 plus one-fifth of x? We broke down the problem, translated it into a mathematical expression, simplified it, and understood what the solution means. We even talked about why these skills are important in the real world. You're well on your way to becoming a math whiz!

Remember, math is like a muscle – the more you exercise it, the stronger it gets. So, keep practicing, keep asking questions, and keep exploring the wonderful world of mathematics. You've got this!