Understanding and Solving Complex Mathematical Expressions: -3 - 2 - 3[2 - 226]×2

Mathematics is a field that often involves the manipulation and evaluation of complex expressions to arrive at a final result. In this article, we will explore how to solve a particular expression: -3 - 2 - 3[2 - 226]×2. We will break down the expression step-by-step, discuss the order of operations, and apply the BODMAS (Brackets, Orders, Division/Multiplication, Addition/Subtraction) rule to understand how to evaluate such expressions accurately.

The Expression and its Components

The given expression is:

-3 - 2 - 3[2 - 226]×2

Step-by-Step Solution

Let's break down the expression step by step:

1.

First, we need to calculate the part inside the brackets:

-2 - 2 2 6 -2 - 2 0 -0 2 6 0 6 8 2.

Next, we multiply the result by 2:

-8 times 2 -16

3.

Substitute the result back into the original expression:

-3 - 2 - 3(-16)

4.

Perform the addition and subtraction from left to right:

-3 - 2 -5 -5 - 3 -8 -8 16 (since -3 * -16 48, but the total is -8 48 32 - 24 8)

Therefore, the final result is:

Answer: 8

Verification: We can verify this by breaking it down further:

- -3 - 2 - 3[2 - 2 2 6] × 2 - -3 - 2 - 3[0 2 6] × 2 - -3 - 2 - 3[8] × 2 - -3 - 2 - 316 - -8 16 8

Order of Operations (BODMAS Rule)

The BODMAS rule (Brackets, Orders, Division/Multiplication, Addition/Subtraction) helps us to evaluate expressions in a systematic way. Here's a breakdown of how it applies to the given expression:

1.

Brackets (B) - We first solve the expression inside the brackets: 2 - 226

2.

Orders (O) - There are no orders (exponents or roots) in this expression.

3.

Division/Multiplication (DM) - We multiply the result by 2.

4.

Addition/Subtraction (AS) - We perform addition and subtraction from left to right.

Conclusion

Solving complex mathematical expressions requires careful attention to the order of operations. By breaking down the expression step-by-step and applying the BODMAS rule, we can arrive at the correct result. The final answer for the given expression -3 - 2 - 3[2 - 226] × 2 is:

Answer: 8

This method can be applied to other similar expressions as well, ensuring accuracy and consistency in your mathematical computations.