(2x-7)/3+(8x-9)/14=(3x-5)/21

2 min read Jun 16, 2024

Solving the Equation: (2x-7)/3 + (8x-9)/14 = (3x-5)/21

This article will guide you through the steps to solve the equation (2x-7)/3 + (8x-9)/14 = (3x-5)/21. We will use the principles of arithmetic and algebraic manipulations to arrive at the solution for 'x'.

Step 1: Find the Least Common Multiple (LCM)

The first step involves finding the LCM of the denominators (3, 14, and 21). The LCM of 3, 14, and 21 is 42.

Step 2: Multiply Each Term by the LCM

Multiply each term of the equation by 42. This eliminates the fractions:

42 * [(2x-7)/3] + 42 * [(8x-9)/14] = 42 * [(3x-5)/21]
This simplifies to: 14(2x-7) + 3(8x-9) = 2(3x-5)

Step 3: Expand the Equation

Expand the equation by multiplying the constants:

28x - 98 + 24x - 27 = 6x - 10

Step 4: Combine Like Terms

Combine the 'x' terms and the constant terms:

(28x + 24x - 6x) = (-10 + 98 + 27)
46x = 115

Step 5: Isolate 'x'

Divide both sides by 46 to isolate 'x':

x = 115/46

Step 6: Simplify the Solution

Simplify the fraction:

x = 5/2

Conclusion

Therefore, the solution to the equation (2x-7)/3 + (8x-9)/14 = (3x-5)/21 is x = 5/2.