Solve Equations: A Step-by-Step Guide

Hey guys! Ever stumbled upon an equation that looks a bit intimidating? Don't sweat it! We're going to break down a math problem, 64 - (P + 6) x 5 = 4, into easy-to-follow steps. This isn't about memorizing formulas; it's about understanding how each part of the equation works and solving it logically. This is a great way to sharpen your math skills, build confidence, and realize that even complex-looking problems are solvable with the right approach. Let's get started, shall we?

Understanding the Equation: Deconstructing the Problem

Before we dive into the solution, let's take a moment to understand what we're dealing with. Our equation, 64 - (P + 6) x 5 = 4, is an algebraic equation. It involves a variable, 'P', which represents an unknown value we need to find. The equation tells us that when we subtract the result of (P + 6) multiplied by 5 from 64, we get 4. The goal is to isolate 'P' to find out its value. The different components of the equation are held together by operations such as subtraction, addition, and multiplication, and understanding the order of operations is key to solving the problem accurately. This is not some complex riddle; it's a structured approach to solving for 'P'. The parentheses indicate that we need to solve this part first. The entire equation is constructed by breaking down the steps. These are building blocks that lead us to the solution. By understanding the structure of the equation, you're already halfway to solving it! We are going to go step by step.

To solve this equation, we need to apply the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). In our equation, we have parentheses, multiplication, subtraction, and addition. Therefore, it is important that we begin with the parentheses, then tackle the multiplication, and finally work through the subtraction and addition. When dealing with equations like this, it helps to think of it as a mathematical puzzle. Each step we take brings us closer to finding the missing value, the solution of 'P'. Let's focus on each operation. We'll keep breaking it down until the value of 'P' is found. Understanding the basic building blocks is important.

Let's break down the different components. The number 64 is a constant, meaning its value does not change. The expression (P + 6) is where the unknown 'P' resides. The multiplication by 5 multiplies the sum of 'P' and 6 by 5. The equal sign (=) indicates that the expression on the left side is equal to the value on the right side, which is 4. Our job is to rearrange the equation to isolate the variable P. We need to do it systematically by performing inverse operations. The initial step is to focus on simplifying the equation, in order to make it easier to solve. This also ensures we maintain balance.

Understanding what the different operations means allows us to move step by step toward the solution. This means understanding the value of P. The aim is to find its value. We need to isolate P to reveal its value. We begin with the outside of the parentheses. This ensures that we solve the equation in the right order. This will ensure we get the correct solution. We work on both sides of the equation to maintain balance. This is an important rule of algebraic equations and must not be forgotten to make sure the end result is the right one. This approach lets us find the correct value for P. It is a step-by-step process. We just need to follow the rules.

Step-by-Step Solution: Breaking Down the Math

Alright, let's get to work! We will solve the equation step by step, making sure we explain each one clearly.

Step 1: Isolate the Term with P

Our first goal is to isolate the term containing 'P', which is (P + 6) x 5. To do this, we need to get rid of the 64 that's being subtracted from it. Remember, we want to isolate the term, so we do the opposite of what's happening to it. In this case, we are subtracting 64 from something to get 4. To undo this, we add 64 to both sides of the equation. This keeps everything balanced. Let's write it out:

Original Equation: 64 - (P + 6) x 5 = 4

Add 64 to both sides: 64 - (P + 6) x 5 + 64 = 4 + 64

This simplifies to:

• (P + 6) x 5 = 60. Remember, the goal is to get the term with 'P' by itself on one side of the equation, the 'P' will be the answer we seek. The aim is to find the value of 'P'. We need to follow each step. We perform this operation on both sides. The goal is to find P. We simplify the equation. The main idea is to eliminate the other numbers and operations. When we add to both sides we are keeping it balanced.

Step 2: Deal with Multiplication

Now, we have -(P + 6) x 5 = 60. The next step is to eliminate the multiplication by -5 from the term (P + 6). To do this, we divide both sides of the equation by -5. Dividing is the inverse of multiplication, we should perform it on both sides. The goal here is to isolate the expression (P + 6). Make sure that you divide both sides. Let's do it step by step. Make sure you are following each step. Let's get it done!

Current Equation: - (P + 6) x 5 = 60

Divide both sides by -5: - (P + 6) x 5 / -5 = 60 / -5

This simplifies to:

(P + 6) = -12

See? We are getting closer to 'P's value. We follow the order of operations and apply inverse operations. Each step brings us closer to the solution. We are dealing with multiplication, it's important to eliminate it. Our goal remains the same, to find the value of P. We follow the steps to get the correct result.

Step 3: Isolate P

We are so close to solving for 'P'! Now we have (P + 6) = -12. The final step is to isolate 'P' by getting rid of the + 6. To do this, we subtract 6 from both sides of the equation. Doing this isolates the variable we need to find. This step will give us the correct value of P.

Current Equation: (P + 6) = -12

Subtract 6 from both sides: P + 6 - 6 = -12 - 6

This simplifies to:

P = -18

We have found the answer!

Verification: Checking Your Work

It's always a good idea to verify your answer to ensure you have solved the problem correctly. Let's substitute P = -18 back into the original equation, 64 - (P + 6) x 5 = 4, and see if it holds true. This step is super important, as it checks our work.

Original Equation: 64 - (P + 6) x 5 = 4

Substitute P = -18: 64 - (-18 + 6) x 5 = 4

Simplify: 64 - (-12) x 5 = 4

Multiply: 64 - (-60) = 4

Solve: 64 + 60 = 4

Which simplifies to: 4 = 4

Since both sides of the equation are equal, we know that our solution, P = -18, is correct. We have proven the answer is correct. This step ensures we haven't made any mistakes. If the values don't match, then something went wrong, and we need to go back and check each step.

Conclusion: Mastering the Equation

And there you have it, guys! We've successfully solved the equation 64 - (P + 6) x 5 = 4. We broke down a complex-looking problem into simple, manageable steps. We've seen how to isolate the variable, apply inverse operations, and verify our answer. Remember, the key to solving these equations is to understand the order of operations, apply inverse operations, and stay organized. We've shown that solving mathematical equations is a matter of following logical steps and understanding the principles involved, not a mysterious process. The more you practice, the easier it will become. Keep up the great work! Now you're ready to tackle similar problems. Good job!