Solving The Equation 20 - M/3 = 11 A Step-by-Step Guide

In the realm of mathematics, solving equations is a fundamental skill. Linear equations, in particular, form the bedrock of algebraic problem-solving. They appear in various contexts, from basic arithmetic to more advanced mathematical concepts. Understanding how to solve them is crucial for success in mathematics and related fields. This article delves into the process of solving the linear equation 20 - m/3 = 11, providing a step-by-step guide to unraveling the unknown variable, m. We'll break down each step with detailed explanations, ensuring that you grasp the underlying principles. We will also explore the importance of understanding the order of operations and applying inverse operations to isolate the variable. This comprehensive guide will equip you with the tools and knowledge necessary to confidently tackle similar equations and deepen your understanding of algebraic concepts. Through clear explanations, examples, and a focus on the fundamental principles, this article empowers you to approach linear equations with confidence and precision.

Before diving into the solution, let's first dissect the equation 20 - m/3 = 11. This equation features a variable, m, which represents the unknown value we aim to determine. The equation involves subtraction and division, linking the variable m with constants. The core challenge lies in isolating m on one side of the equation to reveal its value. To achieve this, we need to understand the structure of the equation and the relationships between its components. The left side of the equation, 20 - m/3, shows that m is being divided by 3, and the result is subtracted from 20. The right side of the equation, 11, is a constant value. The goal of solving this equation is to manipulate it in a way that we can isolate m on one side, while keeping the equation balanced. This involves performing inverse operations to undo the operations that are being applied to m. By understanding the components of the equation and the operations involved, we can develop a strategic approach to solving for m. The process involves careful application of algebraic principles, ensuring that each step maintains the equality of the equation.

The initial step in solving for m involves isolating the term containing the variable, which is -m/3. To do this, we need to eliminate the constant term, 20, from the left side of the equation. Since 20 is being subtracted from -m/3, we apply the inverse operation, which is subtraction. We subtract 20 from both sides of the equation to maintain the balance. This is a critical principle in solving equations: whatever operation you perform on one side, you must perform the same operation on the other side. This ensures that the equality remains true. Subtracting 20 from both sides gives us: 20 - m/3 - 20 = 11 - 20. Simplifying this, we get -m/3 = -9. Now, the term containing m is isolated on the left side, making it easier to proceed with the next step. This step highlights the importance of using inverse operations to undo the operations applied to the variable. By subtracting 20 from both sides, we effectively removed it from the left side, bringing us closer to isolating m. The result, -m/3 = -9, sets the stage for the next step, where we will eliminate the division by 3.

Now that we have the equation -m/3 = -9, our next goal is to eliminate the division by 3. To achieve this, we employ the inverse operation of division, which is multiplication. We multiply both sides of the equation by -3 to undo the division and eliminate the negative sign associated with m. Multiplying both sides by -3 maintains the balance of the equation, a fundamental principle in algebraic manipulations. This step is crucial because it removes the denominator, bringing us closer to isolating m. The careful application of multiplication as the inverse operation of division is a key technique in solving equations involving fractions. By multiplying both sides by -3, we are effectively undoing the division by 3 and the negation of m. This results in a simpler equation that directly reveals the value of m. This step demonstrates the power of inverse operations in simplifying equations and isolating the unknown variable. The result of this step sets the stage for the final determination of the value of m.

After multiplying both sides of the equation by -3, we arrive at the simplified equation m = 27. This final step reveals the solution to the original equation, 20 - m/3 = 11. The value of m that satisfies the equation is 27. To ensure the accuracy of our solution, it's always a good practice to substitute the value of m back into the original equation and verify that the equation holds true. Substituting m = 27 into the original equation, we get: 20 - 27/3 = 11. Simplifying the left side, we have: 20 - 9 = 11, which is indeed true. This verification step confirms that our solution, m = 27, is correct. This process of solving for m demonstrates the systematic approach to handling linear equations. By applying inverse operations step-by-step, we can isolate the variable and determine its value. The ability to solve such equations is a fundamental skill in mathematics, with applications in various fields. Understanding the underlying principles and practicing these techniques will build confidence and proficiency in algebraic problem-solving.

In conclusion, by meticulously following the steps of isolating the variable term, eliminating division, and performing the necessary arithmetic, we have successfully solved the equation 20 - m/3 = 11. The solution we have found is m = 27. This process highlights the power of applying algebraic principles and inverse operations to unravel equations and determine unknown values. The ability to solve linear equations is a fundamental skill that extends beyond the classroom, finding applications in various real-world scenarios. From calculating finances to solving scientific problems, the principles of algebra are essential tools. By mastering these techniques, you equip yourself with the ability to approach mathematical challenges with confidence and precision. This step-by-step guide has provided a clear path to solving the equation, emphasizing the importance of understanding each step and its underlying rationale. The solution m = 27 not only answers the specific problem but also reinforces the broader principles of algebraic problem-solving. By understanding and applying these principles, you can tackle a wide range of mathematical challenges.