Solve for \( r \). \[ 12-\frac{1}{5} r=2 r+1 \]

To solve for \( r \) in the equation \[ 12 - \frac{1}{5} r = 2r + 1, \] first, we can isolate the variable \( r \). Start by moving all \( r \) terms to one side and constant terms to the other. We'll add \( \frac{1}{5} r \) and subtract 1 from both sides: \[ 12 - 1 = 2r + \frac{1}{5} r. \] This simplifies to: \[ 11 = 2r + \frac{1}{5} r. \] Next, we need to combine the \( r \) terms on the right. To do that, we can express \( 2r \) in terms of a fraction with a common denominator: \[ 2r = \frac{10}{5} r, \] so we have: \[ 11 = \frac{10}{5} r + \frac{1}{5} r = \frac{11}{5} r. \] Now, to solve for \( r \), multiply both sides by 5 to eliminate the fraction: \[ 5 \times 11 = 11r, \] which gives: \[ 55 = 11r. \] Now divide by 11: \[ r = 5. \] Thus, the solution is \[ \boxed{5}. \]