-45 Entre (-9)-(-7)(-3)-(-2)-(-3)

by ADMIN 34 views

Solving the Equation: -45 entre (-9)-(-7)(-3)-(-2)-(-3)

In this article, we will delve into the world of mathematics and solve a complex equation step by step. The equation in question is -45 entre (-9)-(-7)(-3)-(-2)-(-3). We will break down the problem into manageable parts, apply the order of operations, and arrive at the final solution.

Before we begin solving the equation, let's take a closer look at what it entails. The equation is a combination of addition, subtraction, multiplication, and division operations. We have a negative number, -45, which is being divided by an expression containing multiple operations.

Breaking Down the Expression

To solve this equation, we need to follow the order of operations, which is Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). Let's break down the expression inside the parentheses first.

Step 1: Evaluate the Expression Inside the Parentheses

The expression inside the parentheses is (-7)(-3). To evaluate this expression, we need to multiply the two negative numbers.

(-7) * (-3) = 21

So, the expression inside the parentheses evaluates to 21.

Step 2: Rewrite the Equation

Now that we have evaluated the expression inside the parentheses, we can rewrite the equation as follows:

-45 entre 21 - (-2) - (-3)

Step 3: Simplify the Equation

Next, we need to simplify the equation by evaluating the expressions inside the parentheses.

-(-2) = 2
-(-3) = 3

So, the equation becomes:

-45 entre 21 - 2 - 3

Step 4: Combine Like Terms

Now, we can combine the like terms in the equation.

-2 - 3 = -5

So, the equation becomes:

-45 entre 21 - 5

Step 5: Evaluate the Division

Finally, we can evaluate the division operation.

-45 entre 21 - 5 = -45 entre 16

Step 6: Simplify the Division

To simplify the division, we can divide the numerator and denominator by their greatest common divisor (GCD).

GCD(-45, 16) = 1

So, the equation remains:

-45 entre 16

Step 7: Final Answer

After simplifying the equation, we arrive at the final answer.

-45 entre 16 = -2.8125

In this article, we solved a complex equation step by step, applying the order of operations and simplifying the expression. We broke down the problem into manageable parts, evaluated the expressions inside the parentheses, combined like terms, and arrived at the final solution. The final answer is -2.8125.

When solving complex equations, it's essential to follow the order of operations and simplify the expression step by step. By breaking down the problem into manageable parts, you can arrive at the final solution more efficiently.

Common Mistakes to Avoid

When solving complex equations, it's easy to make mistakes. Here are some common mistakes to avoid:

  • Not following the order of operations
  • Not simplifying the expression step by step
  • Not combining like terms
  • Not evaluating the division operation correctly

Solving complex equations has numerous real-world applications. Here are a few examples:

  • Finance: Solving complex equations is essential in finance, where you need to calculate interest rates, investment returns, and other financial metrics.
  • Science: Solving complex equations is crucial in science, where you need to model complex systems, predict outcomes, and make informed decisions.
  • Engineering: Solving complex equations is essential in engineering, where you need to design and optimize systems, predict performance, and ensure safety.

In our previous article, we solved a complex equation step by step, applying the order of operations and simplifying the expression. In this article, we will answer some frequently asked questions about solving complex equations.

Q: What is the order of operations?

A: The order of operations is a set of rules that tells you which operations to perform first when you 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: How do I simplify an expression?

A: To simplify an expression, you need to combine like terms and eliminate any unnecessary operations. Here are some steps to follow:

  1. Combine like terms: Combine any terms that have the same variable and coefficient.
  2. Eliminate unnecessary operations: Remove any operations that are not necessary to evaluate the expression.
  3. Simplify fractions: Simplify any fractions in the expression by dividing the numerator and denominator by their greatest common divisor (GCD).

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

A: A variable is a symbol that represents a value that can change. A constant is a value that does not change.

Q: How do I evaluate an expression with multiple operations?

A: To evaluate an expression with multiple operations, you need to follow the order of operations. Here are some steps to follow:

  1. Evaluate any expressions inside parentheses first.
  2. Evaluate any exponential expressions next.
  3. Evaluate any multiplication and division operations from left to right.
  4. Finally, evaluate any addition and subtraction operations from left to right.

Q: What is the greatest common divisor (GCD)?

A: The greatest common divisor (GCD) of two numbers is the largest number that divides both numbers without leaving a remainder.

Q: How do I find the GCD of two numbers?

A: To find the GCD of two numbers, you can use the following steps:

  1. List the factors of each number.
  2. Identify the common factors.
  3. Choose the largest common factor.

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. A quadratic equation is an equation in which the highest power of the variable is 2.

Q: How do I solve a linear equation?

A: To solve a linear equation, you need to isolate the variable on one side of the equation. Here are some steps to follow:

  1. Add or subtract the same value to both sides of the equation to eliminate any constants.
  2. Multiply or divide both sides of the equation by the same value to eliminate any fractions.
  3. Finally, isolate the variable on one side of the equation.

Q: How do I solve a quadratic equation?

A: To solve a quadratic equation, you need to use the quadratic formula. The quadratic formula is:

x = (-b ± √(b^2 - 4ac)) / 2a

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

In conclusion, solving complex equations requires patience, persistence, and attention to detail. By following the order of operations, simplifying the expression step by step, and combining like terms, you can arrive at the final solution more efficiently. Remember to avoid common mistakes and apply the skills you learn to real-world problems.

If you want to learn more about solving complex equations, here are some additional resources:

  • Online tutorials: Websites such as Khan Academy, Coursera, and edX offer online tutorials and courses on solving complex equations.
  • Textbooks: There are many textbooks available on solving complex equations, including "Algebra and Trigonometry" by Michael Sullivan and "College Algebra" by James Stewart.
  • Practice problems: Websites such as Mathway and Wolfram Alpha offer practice problems and exercises on solving complex equations.

In conclusion, solving complex equations is an essential skill that requires practice and patience. By following the order of operations, simplifying the expression step by step, and combining like terms, you can arrive at the final solution more efficiently. Remember to avoid common mistakes and apply the skills you learn to real-world problems.