To solve this equation, we need to first simplify both sides of the equation:
2(x-9)/3 = 3(x-6)/4 - x + 10/6
Simplify the left side:2(x-9)/3 = (2x - 18)/3 = 2x/3 - 6
Simplify the right side:3(x-6)/4 - x + 10/6 = (3x - 18)/4 - x + 5/3 = 3x/4 - 9/2 - x + 5/3
Now we have the equation: 2x/3 - 6 = 3x/4 - 9/2 - x + 5/3
To solve for x, we can combine like terms:
Multiply all terms by 12 to get rid of the fractions:
8x - 72 = 9x - 54 - 6x + 20
Combine like terms:
8x - 72 = 3x - 34
Subtract 3x from both sides:
5x - 72 = -34
Add 72 to both sides:
5x = 38
Divide by 5:
x = 7.6
Therefore, the solution to the equation is x = 7.6.
To solve this equation, we need to first simplify both sides of the equation:
2(x-9)/3 = 3(x-6)/4 - x + 10/6
Simplify the left side:
2(x-9)/3 = (2x - 18)/3 = 2x/3 - 6
Simplify the right side:
3(x-6)/4 - x + 10/6 = (3x - 18)/4 - x + 5/3 = 3x/4 - 9/2 - x + 5/3
Now we have the equation: 2x/3 - 6 = 3x/4 - 9/2 - x + 5/3
To solve for x, we can combine like terms:
Multiply all terms by 12 to get rid of the fractions:
8x - 72 = 9x - 54 - 6x + 20
Combine like terms:
8x - 72 = 3x - 34
Subtract 3x from both sides:
5x - 72 = -34
Add 72 to both sides:
5x = 38
Divide by 5:
x = 7.6
Therefore, the solution to the equation is x = 7.6.