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) ![q](https://tex.z-dn.net/?f=q%3C-13)
Part 6) ![p\geq -121/13](https://tex.z-dn.net/?f=p%5Cgeq%20-121%2F13)
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)
![r\geq -1.817](https://tex.z-dn.net/?f=r%5Cgeq%20-1.817)
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) ![7(q+2)](https://tex.z-dn.net/?f=7%28q%2B2%29%3C-77)
applying distributive property left side
![7q+14](https://tex.z-dn.net/?f=7q%2B14%3C-77)
Subtract 14 both sides
![7q](https://tex.z-dn.net/?f=7q%3C-77-14)
![7q](https://tex.z-dn.net/?f=7q%3C-91)
Divide by 7 both sides
![q](https://tex.z-dn.net/?f=q%3C-91%2F7)
![q](https://tex.z-dn.net/?f=q%3C-13)
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
![13p\geq -121](https://tex.z-dn.net/?f=13p%5Cgeq%20-121)
Divide by 13 both sides
![p\geq -121/13](https://tex.z-dn.net/?f=p%5Cgeq%20-121%2F13)
![p\geq -9.31](https://tex.z-dn.net/?f=p%5Cgeq%20-9.31)
The solution is the interval--------> [-9.31,∞)
The solution in the attached figure N 5