The Art of Algebra: Demystifying the Equation 3 – 3×6 + 2

In the world of mathematics, equations often appear as enigmatic puzzles waiting to be solved. Among these, the equation “3 – 3×6 + 2” stands out as a challenge that beckons us to explore the intricacies of algebraic expressions. In this article, we will unravel the secrets behind this equation, delving into the fundamental principles of algebra and order of operations that govern its solution.

the solution to the equation “3 – 3×6 + 2” is 13.

Understanding the Equation:

At first glance, “3 – 3×6 + 2” might seem perplexing, but with the right approach, we can break down its components. The equation consists of numbers (3 and 6) and mathematical symbols (-, x, +). Understanding the meaning of these symbols and applying the correct order of operations is key to solving the equation.

Order of Operations: PEMDAS

To navigate this equation successfully, we must adhere to the order of operations, often remembered through the acronym PEMDAS:

  • P: Parentheses – simplify expressions within parentheses first, if any.
  • E: Exponents – evaluate powers and square roots.
  • M/D: Multiplication and Division – perform multiplication and division from left to right.
  • A/S: Addition and Subtraction – perform addition and subtraction from left to right.

Solving the Equation Step by Step:

  1. Multiplication: Start by solving the multiplication operation: 3x6=18.
  2. Subtraction: Now, the equation becomes 3−18+23−18+2.
  3. Addition and Subtraction: Proceed to solve addition and subtraction from left to right: 3−18=−153−18=−15, then −15+2=−13−15+2=−13.

Therefore, the solution to the equation “3 – 3×6 + 2” is 13.

Real-Life Applications:

Understanding algebraic expressions like “3 – 3×6 + 2” is not just an academic exercise; it has practical applications in various fields. Engineers use algebra to solve complex problems related to structures and designs. Economists analyze data using algebraic models to understand market trends. Architects employ algebra to create precise blueprints for buildings. In essence, algebra serves as the language of problem-solving in the professional world.

Developing Problem-Solving Skills:

Working through equations like “3 – 3×6 + 2” hones critical thinking and analytical skills. It teaches us to approach challenges systematically, break them down into manageable steps, and apply logical reasoning to find solutions. These problem-solving skills are invaluable, not only in mathematics but also in everyday life situations.

Frequently Asked Questions (FAQ)

1. Why does the order of operations matter in solving this equation?

The order of operations is crucial in mathematics to ensure a standardized way of solving expressions and equations. Following the correct order guarantees that everyone arrives at the same answer.

2. Can I solve the equation in a different order?

No, the order of operations (PEMDAS) is universally accepted in mathematics. Changing the order might lead to a different, incorrect solution. It’s essential to follow the standard rules to ensure accuracy.

3. Why is algebra important in everyday life?

Algebraic skills are valuable for problem-solving in various situations, from calculating finances and making budgetary decisions to understanding patterns and trends in data. It’s a fundamental skill that enhances logical thinking and decision-making abilities.

4. What are some real-world examples where understanding this equation could be useful?

Professions involving calculations, such as engineering, finance, computer science, and architecture, often require algebraic skills. Understanding equations like “3 – 3×6 + 2” is vital in these fields for accurate problem-solving and analysis.

5. How can I improve my algebraic skills?

Practicing regularly, seeking additional resources like textbooks or online tutorials, and solving a variety of equations can significantly enhance algebraic proficiency. Joining study groups or working with a tutor can also provide valuable support.


The equation “3 – 3×6 + 2” might have seemed daunting at first, but by understanding the underlying principles of algebra and following the order of operations, we successfully deciphered its meaning. Algebra, with its ability to model real-world situations and solve complex problems, is an essential tool that empowers us in various fields of study and professions. Embracing the art of algebra equips us with valuable skills, enabling us to approach challenges with confidence and precision. As we delve deeper into the world of mathematics, we continue to unravel the mysteries of equations, one step at a time.

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