To solve the linear equation rac{1}{3}(6u + 3) = 7 - u using the general strategy:

First, simplify each side where possible. Distribute the rac{1}{3} on the left side: $2u + 1 = 7 - u$

Next, collect variable terms on the left side by adding $u$ to both sides: $3u + 1 = 7$

Collect constant terms on the right side by subtracting $1$ from both sides: $3u = 6$

Make the coefficient equal to $1$ by dividing both sides by $3$ to isolate $u$: $u = 2$

Check the answer by substituting $2$ for $u$ in the original equation: rac{1}{3}(6(2) + 3) = rac{1}{3}(12 + 3) = rac{1}{3}(15) = 5 On the right side, $7 - 2 = 5$. Since $5 = 5$, the solution $u = 2$ is verified.