%2F16%2B(2x-3)%2F7%3D(x%2B3)%2F8%2B(3x-1)%2F14.jpeg "(3x+1)/16+(2x-3)/7=(x+3)/8+(3x-1)/14")
Solving the Equation: (3x+1)/16 + (2x-3)/7 = (x+3)/8 + (3x-1)/14
This article will guide you through the process of solving the equation (3x+1)/16 + (2x-3)/7 = (x+3)/8 + (3x-1)/14.
1. Finding the Least Common Multiple (LCM)
To eliminate the fractions, we need to find the least common multiple of the denominators: 16, 7, 8, and 14. The LCM of these numbers is 112.
2. Multiplying Each Term by the LCM
Multiply each term of the equation by 112:
- (112 * (3x+1)/16) + (112 * (2x-3)/7) = (112 * (x+3)/8) + (112 * (3x-1)/14)
This simplifies to:
- 7(3x+1) + 16(2x-3) = 14(x+3) + 8(3x-1)
3. Expanding the Equation
Expand the equation by distributing:
- 21x + 7 + 32x - 48 = 14x + 42 + 24x - 8
4. Combining Like Terms
Combine the terms with x and the constant terms:
- 53x - 41 = 38x + 34
5. Isolating the Variable
Subtract 38x from both sides:
- 15x - 41 = 34
Add 41 to both sides:
- 15x = 75
6. Solving for x
Divide both sides by 15:
- x = 5
Solution
Therefore, the solution to the equation (3x+1)/16 + (2x-3)/7 = (x+3)/8 + (3x-1)/14 is x = 5.