To solve the inequality 2x - 9 > 0:

Add 9 to both sides:

2x - 9 + 9 > 0 + 9

2x > 9

Divide by 2:

x > 4.5

So, the solution to the first inequality is x > 4.5

Now, to solve the inequality 5x + 8 < 0:

Subtract 8 from both sides:

5x + 8 - 8 < 0 - 8

5x < -8

Divide by 5:

x < -1.6

So, the solution to the second inequality is x < -1.6