1) To solve the inequality
(x+2)(x-3)(x-4) < 0

we need to find the critical points where the expression changes sign. These points are when each factor is equal to zero: x = -2, x = 3, x = 4.

This divides the real number line into four intervals:
(-∞, -2), (-2, 3), (3, 4), (4, ∞)

Pick a test point from each interval:
Test x = -3: (-3+2)(-3-3)(-3-4) = (-1)(-6)(-7) = 42 > 0
Test x = 0: (0+2)(0-3)(0-4) = (2)(-3)(-4) = 24 < 0
Test x = 3.5: (3.5+2)(3.5-3)(3.5-4) = (5.5)(0.5)(-0.5) = -1.375 < 0
Test x = 5: (5+2)(5-3)(5-4) = (7)(2)(1) = 14 > 0

Therefore, the solution to the inequality is:
x ∈ (-2, 3) U (4, ∞)

2) To solve the inequality
2x + 1/x + 1 < 1

we first simplify the expression:
2x + 1/x + 1 < 1
2x + 1 + x < x
3x + 1 < x
2x < -1
x < -1/2

Therefore, the solution to the inequality is:
x < -1/2