I need to solve this using the addition and multiplication principle.

5+8x<29

5+8x < 29

subtract 5 from each side, or add -5 to each side to get
5-5 + 8x < 29 -5
8x < 24
We have thus isolated the variable x.
Now we multiply each side by 1/8 in order to reduce the coefficient of x to 1:
(1/8)*8x < 24*(1/8)
x < 24/8
x < 3