Final answer:
The solution to the equation (1/3 + (5/3)r - r = 2r) is r = 1/4, after combining like terms and simplifying the equation.
Step-by-step explanation:
To solve for r in the equation (1/3) + (5/3)r - r = 2r, first simplify and combine like terms:
1. Combine the terms with r: (5/3)r - r - 2r. The common denominator is 3, so convert everything to have the same denominator: (5/3)r - (3/3)r - (6/3)r.
2. Simplify the equation: 5r/3 - 3r/3 - 6r/3 = 5r/3 - 9r/3.
3. This simplifies to: -4r/3 = -1/3.
4. Multiply both sides of the equation by -3/4 to solve for r: r = (-1/3) * (-3/4).
5. Simplify the right side: r = 1/4.
Thus, the solution to the equation is r = 1/4.