(2x-5)/(3x-1)=(2x-1)/(3x+2)

2 min read Jun 16, 2024

Solving the Equation: (2x-5)/(3x-1) = (2x-1)/(3x+2)

This article will guide you through the steps involved in solving the equation (2x-5)/(3x-1) = (2x-1)/(3x+2). We'll use algebraic manipulation to isolate 'x' and find its value.

Step 1: Cross-Multiplication

To begin, we'll cross-multiply the terms in the equation:

(2x-5)(3x+2) = (2x-1)(3x-1)

Step 2: Expanding the Equation

Next, we'll expand both sides of the equation:

6x² + 4x - 15x - 10 = 6x² - 3x - 2x + 1

Step 3: Simplifying the Equation

Combining like terms, we get:

6x² - 11x - 10 = 6x² - 5x + 1

Step 4: Isolating 'x'

To isolate 'x', we'll move all terms containing 'x' to one side of the equation and constant terms to the other:

-11x + 5x = 1 + 10

Step 5: Solving for 'x'

Simplifying the equation, we get:

-6x = 11

Finally, we divide both sides by -6 to find the value of 'x':

x = -11/6

Conclusion

Therefore, the solution to the equation (2x-5)/(3x-1) = (2x-1)/(3x+2) is x = -11/6.