Solve the system of inequalities: 3x > x + 4 4x + 5 > 1

Let's solve each inequality separately:

• First inequality:\[ 3x > x + 4 \]\[ 3x - x > 4 \]\[ 2x > 4 \]\[ x > \frac{4}{2} \]\[ x > 2 \]
• Second inequality:\[ 4x + 5 > 1 \]\[ 4x > 1 - 5 \]\[ 4x > -4 \]\[ x > \frac{-4}{4} \]\[ x > -1 \]

Now, we need to find the values of x that satisfy both conditions (x > 2 AND x > -1).

• If x must be greater than 2, it is automatically greater than -1.
• Therefore, the solution that satisfies both inequalities is x > 2.

Answer: $$\boxed{x > 2}$$