Solving Each Part

When each side of the "or" needs solving, solve them separately and keep the word between them. 2x + 1 < -3 or 3x - 2 > 7:

2x < -4

x < -2

for the first, and

3x > 9

x > 3

for the second. The solution is x < -2 or x > 3, the two rays from the previous lesson.

Each part is an ordinary inequality with the ordinary rules, flips included. The "or" is only the instruction to collect both answers, not to combine them into one.