Answer:
Part 1) [tex]r\geq \sqrt[3]{-6}[/tex]
Part 2) Â [tex]s>4/43[/tex] Â
Part 3) [tex]z\leq6[/tex]
Part 4) Â [tex]t>-7[/tex]
Part 5) [tex]q<-13[/tex]
Part 6) [tex]p\geq -121/13[/tex]
Step-by-step explanation: Â Â Â
Part 1) Â [tex]-r^{3}\leq 6[/tex] Â Â Â Â Â
Multiply by -1 both sides
[tex]r^{3}\geq -6[/tex] Â Â
[tex]r\geq \sqrt[3]{-6}[/tex]
[tex]r\geq -1.817[/tex]
The solution is the interval -------> [-1.817,∞)
The solution in the attached figure N 1 Â Â
Part 2) Â [tex]-4>-43s[/tex] Â Â
rewrite
[tex]-43s<-4[/tex] Â Â Â
Multiply by -1 both sides
 [tex]43s>4[/tex]  Â
 [tex]s>4/43[/tex]   Â
 [tex]s>0.09[/tex]  Â
The solution is the interval--------> (0.09,∞)
The solution in the attached figure N 2
Part 3) [tex]z-2-6\leq-2[/tex]
combine like terms
[tex]z-8\leq-2[/tex] Â
Adds 8 both sides
[tex]z\leq-2+8[/tex]
[tex]z\leq6[/tex]
The solution is the interval--------> (-∞,6]
The solution in the attached figure N 3 Â
Part 4) [tex]-2t-5<9[/tex] Â Â
Adds 5 both sides
[tex]-2t<9+5[/tex]
[tex]-2t<14[/tex]
Multiply by -1 both sides
[tex]2t>-14[/tex]
Divide by 2 both sides
[tex]t>-7[/tex]
The solution is the interval--------> (-7,∞)
The solution in the attached figure N 4 Â
Part 5) [tex]7(q+2)<-77[/tex]
applying distributive property left side
[tex]7q+14<-77[/tex]
Subtract 14 both sides
[tex]7q<-77-14[/tex]
[tex]7q<-91[/tex]
Divide by 7 both sides
[tex]q<-91/7[/tex]
[tex]q<-13[/tex]
The solution is the interval--------> (-∞,-13)
The solution in the attached figure N 5
Part 6) [tex]-13(p+9)\leq4[/tex]
applying distributive property left side
[tex]-13p-117\leq4[/tex]
Adds 117 both sides
[tex]-13p\leq4+117[/tex]
[tex]-13p\leq 121[/tex]
Divide by -1 both sides
[tex]13p\geq -121[/tex]
Divide by 13 both sides
[tex]p\geq -121/13[/tex]
[tex]p\geq -9.31[/tex]
The solution is the interval--------> [-9.31,∞) Â
The solution in the attached figure N 5
