5x - 3 ≥ 17 or -2x + 2 > 8 is a disjunction (the word "or" indicates this) so any number that satisfies either inequality is a solution.
Solve both inequalities:
5x - 3 + 3 ≥ 17 + 3 or - 2x + 2 - 2 > 8 - 2
5x ≥ 20 or -2x > 6
5x ÷ 5 ≥ 20 ÷ 5 or -2x ÷ -2 < 6 ÷ -2 ← if you ÷ (or ×) by neg. # switch sign
x ≥ 4 or x < -3
answer choice A
