To solve these inequalities, we need to factor each expression.

1) x^2 - 10x + 21 > 0
(x - 7)(x - 3) > 0
For x - 7 = 0, x = 7
For x - 3 = 0, x = 3
The critical points are x = 7 and x = 3. We can create a number line with these critical points to determine the solution set:

(-∞, 3) U (7, ∞)

2) 4x^2 + 11x - 3 < 0
(4x - 1)(x + 3) < 0
For 4x - 1 = 0, x = 1/4
For x + 3 = 0, x = -3
The critical points are x = 1/4 and x = -3. We can create a number line with these critical points to determine the solution set:

(-3, 1/4)

3) x^2 - 16 > 0
(x - 4)(x + 4) > 0
For x - 4 = 0, x = 4
For x + 4 = 0, x = -4
The critical points are x = 4 and x = -4. We can create a number line with these critical points to determine the solution set:

(-∞, -4) U (4, ∞)

Therefore, the solutions to the given inequalities are:
1) x ∈ (-∞, 3) U (7, ∞)
2) x ∈ (-3, 1/4)
3) x ∈ (-∞, -4) U (4, ∞)