Answer:
Part 1) ![r\geq \sqrt[3]{-6}](https://tex.z-dn.net/?f=r%5Cgeq%20%5Csqrt%5B3%5D%7B-6%7D)
Part 2)
Part 3)
Part 4)
Part 5) 
Part 6) 
Step-by-step explanation:
Part 1)
Multiply by -1 both sides
![r\geq \sqrt[3]{-6}](https://tex.z-dn.net/?f=r%5Cgeq%20%5Csqrt%5B3%5D%7B-6%7D)

The solution is the interval -------> [-1.817,∞)
The solution in the attached figure N 1
Part 2)
rewrite
Multiply by -1 both sides
The solution is the interval--------> (0.09,∞)
The solution in the attached figure N 2
Part 3)
combine like terms
Adds 8 both sides
The solution is the interval--------> (-∞,6]
The solution in the attached figure N 3
Part 4)
Adds 5 both sides
Multiply by -1 both sides
Divide by 2 both sides
The solution is the interval--------> (-7,∞)
The solution in the attached figure N 4
Part 5) 
applying distributive property left side

Subtract 14 both sides


Divide by 7 both sides


The solution is the interval--------> (-∞,-13)
The solution in the attached figure N 5
Part 6)
applying distributive property left side
Adds 117 both sides
Divide by -1 both sides

Divide by 13 both sides


The solution is the interval--------> [-9.31,∞)
The solution in the attached figure N 5