1)
Simplify the inequality:
4(x-11) - 5(2x-7) < 0
4x - 44 - 10x + 35 < 0
-6x - 9 < 0

Now, let's solve for x:
-6x - 9 < 0
-6x < 9
x > -9/6
x > -3/2

Therefore, the solution to the inequality is x > -3/2.

2)
x|3| > 5
This absolute value inequality can be written as:
x 3 > 5 or x -3 > 5

Solving the first inequality:
x > 5/3

Solving the second inequality:
-3x > 5
x < -5/3

Therefore, the solution to the inequality is x < -5/3 or x > 5/3.