Solve the inequality for \( u \). \[ -5(u+6)+15<2(3-u) \] Simplify your answer as much as possible.

To solve the inequality \(-5(u+6)+15<2(3-u)\), we can start by simplifying both sides. 1. Distribute on the left: \[ -5(u+6) + 15 = -5u - 30 + 15 = -5u - 15. \] 2. Distribute on the right: \[ 2(3-u) = 6 - 2u. \] Now our inequality looks like this: \[ -5u - 15 < 6 - 2u. \] 3. Next, let's get all terms involving \(u\) on one side and the constant terms on the other. We can add \(5u\) to both sides: \[ -15 < 6 - 2u + 5u. \] Simplifying yields: \[ -15 < 6 + 3u. \] 4. Now, subtract \(6\) from both sides: \[ -15 - 6 < 3u. \] This simplifies to: \[ -21 < 3u. \] 5. Finally, divide both sides by \(3\): \[ -7 < u. \] This can also be written as: \[ u > -7. \] So the solution to the inequality is: \[ u > -7. \]