To solve the equation ((3-x/2)-(1-x/3)=7-(x-x/2)), simplify each side separately and then combine like terms. Move the variables to one side and the constants to the other side, and simplify the equation. Divide both sides by the coefficient of x to find the solution.
To solve the equation ((3-x/2)-(1-x/3)=7-(x-x/2)), we need to simplify each side separately and then combine like terms.
- Simplify the left side: ((3-x/2)-(1-x/3)) = ((6-3x)-(2-x)) = (6-3x-2+x) = (4-2x).
- Simplify the right side: (7-(x-x/2)) = (7-(x-1/2x)) = (7-(1/2x)) = (7-1/2x).
- Combine like terms: (4-2x) = (7-1/2x).
- Move the variables to one side and the constants to the other side: -2x+1/2x = 7-4.
- Simplify: -3/2x = 3.
- Divide by -3/2: x = -2.