Solving A Complex Mathematical Expression Step-by-Step

Let's break down this complex mathematical expression step-by-step. It looks intimidating at first, but by tackling each part systematically, we can arrive at the solution.

Part 1: Simplifying the First Term ((-4+9-16-(2-3) 1) × 2)

Okay, let's start with the first big chunk: ((-4+9-16-(2-3) 1) × 2). First, we need to simplify inside the innermost parentheses. Remember your order of operations (PEMDAS/BODMAS) – Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

So, (2-3) equals -1. Now we have: ((-4+9-16-(-1) 1) × 2). That minus a negative becomes plus a positive, so it's ((-4+9-16+1 1) × 2). Let's perform the addition and subtraction from left to right inside the remaining parentheses: -4 + 9 = 5. Then 5 - 16 = -11. Then -11 + 1 = -10. Finally, we have (-10 1) which is just -10. Therefore, we get (-10 × 2) = -20. Guys, this part is done!

This initial simplification is crucial. It sets the stage for handling the rest of the expression. Accuracy in these early steps avoids compounding errors later on. Breaking down the problem into smaller, manageable parts makes the entire process much less daunting.

Remember, mathematical expressions are like puzzles. Each piece fits together in a specific way. By focusing on each individual piece and ensuring its correctness, the complete puzzle becomes solvable.

Part 2: Simplifying the Second Term (15+-3) (7-[2-(-5+4)]+3) × 2-(-12+6)

Now, let's tackle the second term: (15+-3) (7-[2-(-5+4)]+3) × 2-(-12+6). This one's a bit more involved. First, let's simplify (15 + -3), which is the same as 15 - 3, giving us 12. Okay, easy peasy!

Next, let's simplify inside the square brackets: [2-(-5+4)]. Inside those parentheses, -5 + 4 equals -1. So we have [2 - (-1)], which becomes [2 + 1] = 3. Now the expression looks like this: (12) (7 - 3 + 3) × 2 - (-12+6).

Let's continue simplifying inside the parentheses: 7 - 3 + 3 equals 7. So now we have: (12) (7) × 2 - (-12 + 6). Next, let's simplify -12 + 6, which equals -6. Now the expression looks like: (12) (7) × 2 - (-6).

Now we handle the multiplication: 12 × 7 = 84. Then 84 × 2 = 168. So we have: 168 - (-6). Subtracting a negative is the same as adding a positive, so 168 + 6 = 174. Therefore, this entire second term simplifies to 174. Woohoo!

Part 3: Simplifying the Third Term ((-3 +7-[4-(-2 + 1)]) × 2) - (-6 + 3)

Alright, let's dive into the third term: ((-3 +7-[4-(-2 + 1)]) × 2) - (-6 + 3). Starting inside the innermost parentheses: -2 + 1 = -1. Now we have: ((-3 +7-[4-(-1)]) × 2) - (-6 + 3).

Next, simplify inside the square brackets: [4 - (-1)] becomes [4 + 1] = 5. Now the expression is: ((-3 + 7 - 5) × 2) - (-6 + 3). Let's simplify inside the remaining parentheses from left to right: -3 + 7 = 4. Then 4 - 5 = -1. Now we have ((-1) × 2) - (-6 + 3).

Continuing with the parentheses: (-1 × 2) = -2. Now we have: -2 - (-6 + 3). Let's simplify the remaining parentheses: -6 + 3 = -3. So the expression is now: -2 - (-3). Subtracting a negative is the same as adding a positive, so -2 + 3 = 1. Therefore, this entire third term simplifies to 1.

Simplifying each part step by step minimizes errors and makes complex problems manageable. It allows us to focus on each operation individually, ensuring precision.

Part 4: Combining the Simplified Terms

Now that we've simplified each term, let's put it all together. We found that:

• Term 1 simplifies to -20
• Term 2 simplifies to 174
• Term 3 simplifies to 1

So the original expression now becomes: -20 + 174 + 1.

Let's do the addition: -20 + 174 = 154. Then, 154 + 1 = 155. Therefore, the final answer is 155. Awesome!

Final Answer: 155

So, after meticulously breaking down the original expression and simplifying each component, the final answer is 155. Remember, the key to tackling complex mathematical problems is to take it one step at a time and double-check your work along the way. Great job, guys! We conquered that beast of an equation!

Breaking down complex equations into smaller, manageable parts is crucial. This approach simplifies the process and reduces the chance of errors. Furthermore, meticulous attention to each step ensures accurate calculations and a reliable final result. Using PEMDAS/BODMAS, we've navigated through parentheses, brackets, and various mathematical operations, arriving at the solution with confidence.

Moreover, this exercise highlights the importance of a systematic approach in problem-solving. By focusing on individual components and ensuring their correctness, we create a solid foundation for the subsequent steps. Each part is treated as a separate puzzle, which, when solved, contributes to the overall solution.

Finally, consider the real-world applications of such skills. Whether you're managing finances, designing structures, or conducting scientific research, the ability to simplify and solve complex problems is invaluable. This mathematical workout is not just about numbers; it's about developing critical thinking and problem-solving skills applicable across diverse fields.