3x-4 Value When X = 7? Solve It Now!

by Luna Greco 37 views

Hey guys! Let's dive into this math problem together. We've got a straightforward algebraic expression here, and our mission is to figure out its value when we know the value of 'x'. So, let's break it down step by step. This will be a fun and easy journey through basic algebra, perfect for anyone looking to brush up on their skills or just understand how these things work. We'll go through the problem, explore the concepts involved, and make sure everyone's on the same page. Ready? Let's get started!

Breaking Down the Problem

Our main task is to evaluate the expression 3x - 4 when x equals 7. This means we're going to substitute the value 7 in place of x in the expression. It's like swapping out a placeholder with the real thing. Think of x as a mystery number, and now we know what that mystery number is! Once we make the substitution, we'll just need to do some simple arithmetic to find the final answer. This type of problem is a classic example of evaluating algebraic expressions, a fundamental skill in algebra. It's all about following the order of operations and making sure we substitute correctly. So, let's get into the nitty-gritty details and see how it's done.

Step-by-Step Solution

  1. Substitution: The first thing we need to do is replace the x in our expression with the number 7. So, 3x - 4 becomes 3(7) - 4. See how we just swapped out the x with its value? This is the crucial first step in solving this problem. It's like plugging in the right piece of the puzzle. Without this substitution, we can't move forward. Make sure you understand this step perfectly before moving on, because it's the foundation for the rest of the solution.
  2. Multiplication: Next up, we need to handle the multiplication. In the expression 3(7) - 4, the 3(7) means 3 times 7. When we multiply these together, we get 21. So, our expression now looks like 21 - 4. We've taken care of the multiplication part, which is a key step in the order of operations (remember PEMDAS/BODMAS?). Now we're one step closer to finding the final answer. Keep following along, and you'll see how simple it is to break down these kinds of problems.
  3. Subtraction: Finally, we have a simple subtraction problem left: 21 - 4. When we subtract 4 from 21, we get 17. So, the value of the expression 3x - 4 when x is 7 is 17. That's it! We've solved the problem. It's amazing how a seemingly complex expression can be simplified down to a single number with just a few steps. This is the power of algebra, and you've just seen it in action. Great job!

Putting It All Together

So, to recap, we started with the expression 3x - 4 and the value x = 7. We substituted 7 for x, which gave us 3(7) - 4. Then, we performed the multiplication: 3 times 7 equals 21, so we had 21 - 4. Finally, we did the subtraction: 21 minus 4 equals 17. Therefore, the value of 3x - 4 when x is 7 is 17. We found our answer by following a clear, step-by-step process. This is how you tackle algebraic expressions—break them down into smaller, manageable parts. With practice, you'll become a pro at solving these types of problems. Keep going, and you'll master algebra in no time!

Understanding the Basics of Algebra

Algebra is like a secret code where letters and symbols represent numbers. It's a super useful tool for solving problems where you don't know all the information. Think of it as a puzzle where you're trying to find the missing pieces. In our problem, x was the mystery number we needed to figure out. Algebraic expressions are made up of terms, which can be numbers, variables (like x), or a combination of both. These terms are connected by mathematical operations like addition, subtraction, multiplication, and division. Learning algebra is like learning a new language, but once you get the hang of it, you can unlock all sorts of cool mathematical mysteries. So, let's dive deeper into some key algebraic concepts.

Variables and Constants

In algebra, we often use letters to represent numbers that can change or that we don't know yet. These letters are called variables. In our problem, x is a variable. It can take on different values, and in this case, it was equal to 7. Variables are like placeholders that can stand in for any number. On the other hand, constants are numbers that don't change. In the expression 3x - 4, 3 and 4 are constants. They stay the same no matter what value x has. Understanding the difference between variables and constants is crucial for working with algebraic expressions. It's like knowing the players on a team—each has a specific role.

Expressions and Equations

An expression is a combination of variables, constants, and operations, like 3x - 4. It represents a mathematical relationship, but it doesn't necessarily have an equals sign. An equation, on the other hand, is a statement that two expressions are equal. For example, 3x - 4 = 17 is an equation. Equations always have an equals sign, and they often involve solving for a variable. Think of an expression as a phrase and an equation as a sentence. The equation tells us that two things are the same, and our job is often to find the value of the variable that makes the equation true. In our problem, we were given an expression and a value for x, and we had to evaluate the expression.

Order of Operations

When we're working with algebraic expressions, it's super important to follow the correct order of operations. This is a set of rules that tells us which operations to perform first. You might have heard of the acronyms PEMDAS or BODMAS, which help us remember the order: Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). In our problem, we first did the multiplication (3 * 7) and then the subtraction (21 - 4). Following the order of operations ensures that we get the correct answer every time. It's like following a recipe—if you skip a step, the dish might not turn out right!

Real-World Applications of Algebra

Algebra isn't just something you learn in a classroom; it's actually super useful in everyday life! You might not even realize it, but you're probably using algebraic thinking all the time. Let's look at some cool real-world examples where algebra comes in handy. From calculating costs to planning trips, algebra helps us make sense of the world around us. It's like having a superpower for problem-solving!

Calculating Costs

Imagine you're buying several items at a store. Each item costs the same amount, and you also have a coupon for a certain amount off. Algebra can help you figure out the total cost. Let's say you're buying 5 items that each cost x dollars, and you have a coupon for $3 off. The total cost can be represented by the expression 5x - 3. If each item costs $4, then x = 4, and the total cost would be 5(4) - 3 = 20 - 3 = $17. See how algebra helps you calculate the total cost quickly and easily? This is just one example of how algebra can be used in shopping and budgeting.

Planning Trips

Algebra can also help you plan trips. Suppose you're driving to a destination that's a certain distance away, and you want to know how long it will take. Let's say the distance is d miles, and you're driving at an average speed of r miles per hour. The time it will take to get there, t, can be calculated using the formula t = d / r. For example, if you're driving 300 miles at 60 miles per hour, then t = 300 / 60 = 5 hours. Algebra helps you estimate travel times so you can plan your trips effectively. It's like having a built-in GPS for your brain!

Solving Puzzles and Games

Many puzzles and games involve algebraic thinking. Sudoku, for example, requires you to use logic and reasoning to fill in missing numbers. Cryptograms, where letters stand for other letters, also involve algebraic problem-solving skills. Even video games often use algebraic equations to calculate trajectories, speeds, and other variables. So, the next time you're playing a game or solving a puzzle, remember that you're using algebra! It's a fun way to practice your math skills without even realizing it.

Practice Problems

Alright, guys, it's time to put your new algebra skills to the test! Practice is key to mastering any math concept, so let's work through a few more problems together. These practice problems will help you solidify your understanding of evaluating expressions. Remember, the more you practice, the more confident you'll become. So, grab a pencil and paper, and let's get started!

Problem 1

Evaluate the expression 2x + 5 when x = 3. Can you figure it out? Take a moment to work through the steps we discussed earlier. Remember to substitute the value of x and follow the order of operations. Once you have your answer, compare it with the solution below.

Solution:

  1. Substitute: 2(3) + 5
  2. Multiply: 6 + 5
  3. Add: 11

So, the value of the expression 2x + 5 when x = 3 is 11. Did you get it right? Great job!

Problem 2

What is the value of 4y - 7 when y = 6? This problem is similar to the first one, but with different numbers. Follow the same steps: substitute, multiply, and then subtract. Don't rush; take your time and think through each step. Ready? Go!

Solution:

  1. Substitute: 4(6) - 7
  2. Multiply: 24 - 7
  3. Subtract: 17

The value of the expression 4y - 7 when y = 6 is 17. Awesome! You're getting the hang of this.

Problem 3

Evaluate 5(z - 2) when z = 8. This problem has parentheses, so remember to do what's inside the parentheses first. This is where the order of operations (PEMDAS/BODMAS) really comes into play. You've got this!

Solution:

  1. Substitute: 5(8 - 2)
  2. Parentheses: 5(6)
  3. Multiply: 30

The value of the expression 5(z - 2) when z = 8 is 30. Excellent work! You tackled the parentheses like a pro.

Conclusion

So, guys, we've reached the end of our algebraic adventure! We started with a simple question: What is the value of 3x - 4 when x = 7? And we journeyed through substitution, multiplication, subtraction, and the order of operations to find the answer: 17. But more than just finding the answer, we've explored the amazing world of algebra. We've learned about variables, constants, expressions, equations, and how algebra is used in real-life situations. You've practiced solving problems and built a solid foundation for future math challenges. Remember, algebra is like a language—the more you practice, the more fluent you'll become. So, keep exploring, keep practicing, and keep unlocking the power of math! You've got this!