3/2[3(4/5+1/3)-1(2-4)/2]​

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Solving the Complex Equation: 3/2[3(4/5+1/3)-1(2-4)/2]

In this article, we will delve into the world of complex equations and explore the solution to the equation 3/2[3(4/5+1/3)-1(2-4)/2]. This equation may seem daunting at first, but with a step-by-step approach, we can break it down and find the solution. We will use mathematical operations and formulas to simplify the equation and arrive at the final answer.

Understanding the Equation

The given equation is 3/2[3(4/5+1/3)-1(2-4)/2]. To solve this equation, we need to follow the order of operations (PEMDAS):

  1. Evaluate the expressions inside the parentheses.
  2. Multiply and divide from left to right.
  3. Add and subtract from left to right.

Step 1: Evaluate the Expressions Inside the Parentheses

Let's start by evaluating the expressions inside the parentheses:

  • 4/5 + 1/3
  • 2 - 4

To add or subtract fractions, we need to have a common denominator. The least common multiple (LCM) of 5 and 3 is 15. So, we can rewrite the fractions as:

  • 4/5 = 12/15
  • 1/3 = 5/15

Now, we can add the fractions:

  • 12/15 + 5/15 = 17/15

Similarly, we can rewrite the second expression as:

  • 2 - 4 = -2

Step 2: Simplify the Equation

Now that we have evaluated the expressions inside the parentheses, we can simplify the equation:

3/2[3(17/15)-1(-2)/2]

To simplify the equation further, we can multiply the numbers outside the parentheses:

  • 3/2 = 3/2
  • 3(17/15) = 51/15
  • 1(-2)/2 = -1

Now, we can rewrite the equation as:

3/2[51/15 - (-1)]

Step 3: Simplify the Expression Inside the Square Brackets

To simplify the expression inside the square brackets, we need to follow the order of operations:

  • Subtract -1 from 51/15:
    • 51/15 - (-1) = 51/15 + 1 = 66/15
  • Multiply 3/2 by 66/15:
    • 3/2 × 66/15 = 198/30

Step 4: Simplify the Final Expression

Now that we have simplified the expression inside the square brackets, we can simplify the final expression:

198/30 = 33/5

In this article, we solved the complex equation 3/2[3(4/5+1/3)-1(2-4)/2] using mathematical operations and formulas. We followed the order of operations (PEMDAS) and simplified the equation step by step. The final solution is 33/5.

The final answer is 33/5.

If you are struggling with complex equations, here are some additional tips and resources:

  • Use a calculator or online tool to help you simplify the equation.
  • Break down the equation into smaller parts and solve each part separately.
  • Use mathematical formulas and operations to simplify the equation.
  • Practice solving complex equations to improve your skills.

When solving complex equations, here are some common mistakes to avoid:

  • Not following the order of operations (PEMDAS).
  • Not simplifying the equation step by step.
  • Not using mathematical formulas and operations to simplify the equation.
  • Not practicing solving complex equations to improve your skills.

Complex equations have many real-world applications, including:

  • Physics and engineering: Complex equations are used to describe the behavior of physical systems, such as the motion of objects and the flow of fluids.
  • Computer science: Complex equations are used to solve problems in computer science, such as the traveling salesman problem and the knapsack problem.
  • Economics: Complex equations are used to model economic systems and make predictions about economic trends.

Q: What is a complex equation?

A: A complex equation is an equation that involves multiple mathematical operations, such as addition, subtraction, multiplication, and division, as well as variables and constants.

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

A: Following the order of operations (PEMDAS) is crucial when solving complex equations because it ensures that mathematical operations are performed in the correct order. This helps to avoid errors and ensures that the equation is solved correctly.

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 remains the same.

Q: How do I simplify a complex equation?

A: To simplify a complex equation, follow these steps:

  1. Evaluate the expressions inside the parentheses.
  2. Multiply and divide from left to right.
  3. Add and subtract from left to right.

Q: What is the least common multiple (LCM)?

A: The least common multiple (LCM) is the smallest number that is a multiple of two or more numbers.

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

A: To find the LCM of two numbers, list the multiples of each number and find the smallest number that is common to both lists.

Q: What is the difference between a fraction and a decimal?

A: A fraction is a way of expressing a part of a whole, while a decimal is a way of expressing a number as a sum of powers of 10.

Q: How do I convert a fraction to a decimal?

A: To convert a fraction to a decimal, divide the numerator by the denominator.

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 a linear equation?

A: To solve a linear equation, follow these steps:

  1. Isolate the variable on one side of the equation.
  2. Add or subtract the same value to both sides of the equation.
  3. Multiply or divide both sides of the equation by the same value.

Q: How do I solve a quadratic equation?

A: To solve a quadratic equation, follow these steps:

  1. Factor the equation, if possible.
  2. Use the quadratic formula to find the solutions.
  3. Check the solutions to ensure that they are valid.

Q: What is the quadratic formula?

A: The quadratic formula is a formula that is used to find the solutions to a quadratic equation. The formula is:

x = (-b ± √(b^2 - 4ac)) / 2a

Q: What is the difference between a rational number and an irrational number?

A: A rational number is a number that can be expressed as a ratio of two integers, while an irrational number is a number that cannot be expressed as a ratio of two integers.

Q: How do I determine if a number is rational or irrational?

A: To determine if a number is rational or irrational, try to express it as a ratio of two integers. If you can, then the number is rational. If you cannot, then the number is irrational.

In conclusion, solving complex equations requires a deep understanding of mathematical operations and formulas. By following the order of operations (PEMDAS) and simplifying the equation step by step, we can arrive at the final solution. With practice and patience, you can become proficient in solving complex equations and apply them to real-world problems.