Solving the Equation 2a - 1 3a1

Algebra is an essential branch of mathematics used in solving various equations. This article will delve into the process of solving the equation 2a - 1 3a1, with a detailed step-by-step explanation, proof, and verification of the solution. Understanding this process can significantly enhance your problem-solving skills in algebra.

Introduction to the Equation

An equation is a mathematical statement that equates two expressions. In this case, we are dealing with the equation 2a - 1 3a1. This equation involves a variable a, and our goal is to find the value of a.

Step-by-Step Solution

Let's break down the solution step by step:

Start with the original equation: 2a - 1 3a1 Observe that the term 3a1 can be simplified: 3a1 3a (Assuming '1' is a coefficient) Substitute 3a1 with 3a: 2a - 1 3a Isolate the variable terms on one side: 2a - 3a 1 Combine like terms: -a 1 Divide both sides by -1: a -1 Upon closer inspection, it appears that the solution might have been incorrect based on the initial premise. Let's re-evaluate the equation.

Re-evaluation of the Equation

Upon re-evaluating the equation, we find that the term 3a1 can be directly substituted to 3a, leading to:

2a - 1 3a Bring all terms involving 'a' to one side: 2a - 3a 1 Simplify the left side: -a 1 Divide both sides by -1 to solve for 'a': a -1

Verification of the Solution

To verify the solution, let's substitute a -1 back into the original equation:

2a - 1 3a1

LHS (Left Hand Side):
2(-1) - 1 -2 - 1 -3

RHS (Right Hand Side):
3(-1)1 3(-1) -3

Since LHS RHS, the solution a -1 is indeed correct.

Conclusion

Through careful step-by-step solution and verification, we have determined that the solution to the equation 2a - 1 3a1 is a -1. Understanding and verifying solutions are crucial in solving algebraic equations, ensuring accuracy and consistency in mathematical problem-solving.

Keywords: algebra, equation solving, variable substitution