Linear equations in one variable form the foundation of algebra. These are equations that involve a single variable raised to the power of 1, such as x + 5 = 12. Solving such equations means finding the value of the variable that makes the equation true.
This video provides a step-by-step explanation of how to solve linear equations in one variable using two powerful techniques: the law of transposition and ancient Vedic math sutras.
Transposition is a basic algebraic rule that allows us to move a term from one side of the equation to the other by changing its sign. This makes it easier to isolate the variable and solve the equation efficiently.
Example: Find the value of x in the equation 2x + 3 = 11.
Step 1: Move 3 to the other side of the equation: 2x = 11 - 3
Step 2: Simplify: 2x = 8
Step 3: Divide both sides by 2: x = 4
This straightforward approach can be applied to any linear equation in one variable, regardless of how complicated the equation might first appear.
Vedic Mathematics offers intuitive and fast ways to approach algebraic problems. One of the relevant sutras is "Sankalana-Vyavakalanabhyam" (by addition and subtraction), which promotes the idea of balancing both sides with minimum steps.
Example using Vedic Logic: For the same equation, 2x + 3 = 11, think in terms of balance:
What added to 3 gives 11? The answer is 8. Then, what times 2 gives 8? The answer is 4.
Therefore, x = 4—found without traditional step-by-step transposition.
Such mental shortcuts are valuable, especially in exams or when quick thinking is needed.
Understanding how to solve linear equations in one variable is a key algebra skill. Whether you use the structured approach of transposition or the intuitive methods from Vedic Mathematics, mastering both can make problem-solving quicker and more insightful.
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