7) \( 3(t-3)=5(2 t+1) \)

To solve the equation \( 3(t-3)=5(2 t+1) \), let's first distribute both sides. On the left, we have \( 3t - 9 \), and on the right, it's \( 10t + 5 \). Thus, we get the equation: \[ 3t - 9 = 10t + 5 \] Next, we can rearrange the equation by moving all terms involving \( t \) to one side and constant terms to the other: \[ 3t - 10t = 5 + 9 \] This simplifies to: \[ -7t = 14 \] Now, divide both sides by -7: \[ t = -2 \] And there we have it! The solution to the equation is \( t = -2 \).