Solving P X (8 + 4) - 20 = 40: A Step-by-Step Guide

Are you scratching your head over the equation P x (8 + 4) - 20 = 40? Don't sweat it, guys! Equations might seem intimidating, but breaking them down step-by-step makes them totally manageable. In this guide, we'll walk through solving this equation, ensuring you understand each move. We will cover the methods and explain the logic behind them, so you can conquer similar problems with confidence. Let's dive in and make solving equations a breeze. This equation is a classic example of a linear equation involving a single variable, P. The goal is to isolate the variable P on one side of the equation to find its value. We'll use the order of operations (PEMDAS/BODMAS) to ensure we perform calculations in the correct sequence, leading us to the accurate solution. We'll cover the basic principles of algebraic manipulation to simplify and solve the equation. These include using inverse operations (addition/subtraction and multiplication/division) to maintain the equation's balance, ensuring the value on one side equals the value on the other. Each step is designed to build your understanding, enabling you to confidently handle more complex equations in the future. So, grab your pencils and let's start solving this equation. We'll be using the order of operations (PEMDAS/BODMAS), which dictates the sequence of operations to be performed. It's really just a set of rules that make sure we all get the same answer. We're going to start by dealing with the parentheses first, which is where the 8 + 4 is hanging out. Then we'll move on to the multiplication. After that, it's all about isolating P. Sound good? Let's get to it.

Step-by-Step Solution of the Equation

Let's start breaking down the equation P x (8 + 4) - 20 = 40. We'll go step by step to make sure we understand every move. Remember, the key to solving equations is to do the same thing to both sides to keep things balanced. This ensures that the equation remains true as we simplify it. We'll start by simplifying the expression inside the parentheses. This is usually the first thing we do, according to PEMDAS/BODMAS. Then, we'll move on to the multiplication and then deal with the subtraction. The ultimate goal is to isolate P and find out what it equals. Keep in mind that each step is important, and they build on each other. By following these steps carefully, you'll be able to solve this equation and understand the underlying concepts. It might seem like a lot of steps at first, but with a little practice, it will become second nature. Let's get started!

Step 1: Simplify Inside the Parentheses

First things first, let's tackle what's inside the parentheses. In the equation P x (8 + 4) - 20 = 40, we have (8 + 4). According to PEMDAS/BODMAS, we need to do this first. So, what's 8 + 4? That's right, it's 12. Now, our equation looks like this: P x 12 - 20 = 40. This initial simplification is critical because it reduces the complexity of the equation, allowing us to focus on the remaining operations. Simplifying inside the parentheses is a basic operation. It doesn't change the essence of the equation, but it makes the equation easier to look at and continue. By making the simplification, we've just reduced the equation to a simpler form. Now, we have fewer terms to worry about and we're one step closer to solving the equation. This step also reinforces the concept of order of operations, which is the foundation of solving equations. Make sure you take note of this step; it is very important.

Step 2: Rewrite the Equation

Now that we've simplified the parentheses, let's rewrite the equation to reflect the change. Remember, in Step 1, we simplified (8 + 4) to 12. So, the equation P x (8 + 4) - 20 = 40 becomes P x 12 - 20 = 40. This is a cleaner, more manageable version of our original equation. When rewriting the equation, we're making it easier to solve by reducing the number of operations. Rewrite it carefully because that changes everything that comes next. By rewriting it, we've removed the parentheses and combined the numbers inside, making it look less intimidating. Remember, every step counts when solving an equation. Rewrite carefully and do it right, because it's all about accuracy. We are getting closer to solving for P. So make sure you stay focused, and pay attention to every little detail.

Step 3: Isolate the Term with P

Our next move is to get the term with P by itself. In the equation P x 12 - 20 = 40, the term with P is 'P x 12'. To isolate this term, we need to get rid of the -20. We do this by adding 20 to both sides of the equation. Why? Because adding 20 to the left side cancels out the -20, and to keep the equation balanced, we have to add 20 to the right side as well. So, the equation becomes P x 12 - 20 + 20 = 40 + 20. This step is crucial because it moves us closer to getting P by itself. By using inverse operations, we maintain the equality of the equation. This step demonstrates the fundamental concept of balance in equations. The goal here is to isolate P on one side so that we can determine its value. Now the equation is simpler and one step closer to the final result. Adding 20 to both sides of the equation ensures that our equation is balanced and will still be true when we solve for P. Remember, whatever you do to one side, you do to the other.

Step 4: Simplify Further

Let's simplify the equation we got in Step 3: P x 12 - 20 + 20 = 40 + 20. On the left side, -20 + 20 cancels out, leaving us with just P x 12. On the right side, 40 + 20 equals 60. So, after simplifying, our equation now looks like this: P x 12 = 60. Simplifying the equation makes it easier to solve. This step consolidates our previous manipulations, giving us a clearer path to the final solution. At this point, we're essentially trimming down the equation to its bare essentials, making it easier to solve. The simpler it gets, the easier it is to solve for P. Now we are one step closer to finding the solution! Make sure you stay focused because the final result is coming up.

Step 5: Solve for P

We're in the home stretch now! We have the equation P x 12 = 60. To solve for P, we need to get P by itself. Since P is being multiplied by 12, we do the opposite: divide both sides of the equation by 12. So, we have (P x 12) / 12 = 60 / 12. On the left side, the 12s cancel out, leaving us with just P. On the right side, 60 divided by 12 equals 5. Therefore, P = 5. And there you have it! We've successfully solved for P. This step is the final step where we use division to isolate P and determine its value. This step exemplifies the use of inverse operations to isolate the variable. The final result shows the true value of P. We have finally determined the value of P. Great job!

Conclusion

So, we've walked through solving the equation P x (8 + 4) - 20 = 40, step by step. By following the order of operations, simplifying each step, and using inverse operations, we've found that P = 5. Remember, mastering equations like these comes with practice. The more you work through these kinds of problems, the more comfortable you'll become. Always remember to break the problem into smaller parts, do the same thing to both sides of the equation, and check your work. Equations might seem scary at first, but with a little effort and a good approach, they're totally conquerable. If you practice regularly and keep at it, you'll be solving equations with confidence in no time. Keep going, and you'll master equations like a pro. Don't be afraid to ask for help when you need it. Practice is key, and you will do it! So, keep up the great work, and keep solving equations!