50÷{2×[-7+18+(-3+12)]}-[7×(-3)-18÷(-2)+1]=

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Introduction

Mathematical equations can be complex and challenging to solve, especially when they involve multiple operations and variables. In this article, we will explore a specific equation that requires careful analysis and step-by-step solving. The equation is: 50÷{2×[-7+18+(-3+12)]}-[7×(-3)-18÷(-2)+1]=. We will break down the equation into smaller parts, solve each part, and then combine the results to find the final answer.

Understanding the Equation

The given equation is a combination of arithmetic operations, including division, multiplication, addition, and subtraction. To solve it, we need to follow the order of operations (PEMDAS):

  1. Parentheses: Evaluate expressions inside parentheses first.
  2. Exponents: Evaluate any exponential expressions next.
  3. Multiplication and Division: Evaluate multiplication and division operations from left to right.
  4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Breaking Down the Equation

Let's break down the equation into smaller parts and solve each part step by step:

Part 1: Evaluating the Expression Inside the Parentheses

The expression inside the parentheses is: -7+18+(-3+12)

-7 + 18 + (-3 + 12)

To evaluate this expression, we need to follow the order of operations:

  1. Evaluate the expression inside the inner parentheses: -3 + 12 = 9
  2. Add 18 to the result: 18 + 9 = 27
  3. Subtract 7 from the result: 27 - 7 = 20

So, the expression inside the parentheses evaluates to 20.

Part 2: Evaluating the Expression Inside the Brackets

The expression inside the brackets is: 2×20

2 × 20

To evaluate this expression, we simply multiply 2 by 20, which gives us 40.

Part 3: Evaluating the Expression Inside the Brackets (Again)

The expression inside the brackets is: 7×(-3)-18÷(-2)+1

7 × (-3) - 18 ÷ (-2) + 1

To evaluate this expression, we need to follow the order of operations:

  1. Multiply 7 by -3: 7 × (-3) = -21
  2. Divide 18 by -2: 18 ÷ (-2) = -9
  3. Subtract -9 from -21: -21 - (-9) = -12
  4. Add 1 to the result: -12 + 1 = -11

So, the expression inside the brackets evaluates to -11.

Part 4: Combining the Results

Now that we have evaluated all the expressions, we can combine the results to find the final answer:

50÷40 - (-11)

50 ÷ 40 - (-11)

To evaluate this expression, we need to follow the order of operations:

  1. Divide 50 by 40: 50 ÷ 40 = 1.25
  2. Subtract -11 from the result: 1.25 - (-11) = 1.25 + 11 = 12.25

So, the final answer is 12.25.

Conclusion

Introduction

Solving complex mathematical equations can be a challenging task, especially for those who are new to mathematics or are not familiar with the order of operations. In this article, we will answer some frequently asked questions (FAQs) about solving complex mathematical equations, including the equation we solved in our previous article: 50÷{2×[-7+18+(-3+12)]}-[7×(-3)-18÷(-2)+1]=.

Q: What is the order of operations?

A: The order of operations is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. The order of operations is:

  1. Parentheses: Evaluate expressions inside parentheses first.
  2. Exponents: Evaluate any exponential expressions next.
  3. Multiplication and Division: Evaluate multiplication and division operations from left to right.
  4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: Why is it important to follow the order of operations?

A: Following the order of operations is important because it ensures that we perform the operations in the correct order and get the correct result. If we don't follow the order of operations, we may get a different result, which can lead to errors and confusion.

Q: How do I evaluate expressions inside parentheses?

A: To evaluate expressions inside parentheses, we need to follow the order of operations inside the parentheses. We start by evaluating any exponential expressions, then any multiplication and division operations, and finally any addition and subtraction operations.

Q: What is the difference between multiplication and division?

A: Multiplication and division are both operations that involve numbers, but they have different properties and behaviors. Multiplication is a commutative operation, which means that the order of the numbers doesn't matter. Division, on the other hand, is a non-commutative operation, which means that the order of the numbers does matter.

Q: How do I evaluate expressions with multiple operations?

A: To evaluate expressions with multiple operations, we need to follow the order of operations. We start by evaluating any expressions inside parentheses, then any exponential expressions, then any multiplication and division operations, and finally any addition and subtraction operations.

Q: What is the difference between a variable and a constant?

A: A variable is a symbol that represents a value that can change, while a constant is a value that doesn't change. Variables are often represented by letters such as x, y, or z, while constants are often represented by numbers.

Q: How do I solve equations with variables?

A: To solve equations with variables, we need to isolate the variable on one side of the equation. We can do this by adding, subtracting, multiplying, or dividing both sides of the equation by the same value.

Q: What is the difference between a linear equation and a quadratic equation?

A: A linear equation is an equation in which the highest power of the variable is 1, while a quadratic equation is an equation in which the highest power of the variable is 2.

Q: How do I solve quadratic equations?

A: To solve quadratic equations, we can use the quadratic formula, which is:

x = (-b ± √(b² - 4ac)) / 2a

where a, b, and c are the coefficients of the quadratic equation.

Conclusion

Solving complex mathematical equations requires careful analysis and attention to detail. By following the order of operations and understanding the properties of different operations, we can evaluate expressions and solve equations with confidence. We hope that this article has helped to answer some of your questions about solving complex mathematical equations. If you have any further questions, please don't hesitate to ask.