Question

1.)Solve the inequality. Graph the solution.

Answer 1

Answer:

Part 1) $r\geq \sqrt[3]{-6}$

Part 2)   $s>4/43$  

Part 3) $z\leq6$

Part 4)  $t>-7$

Part 5) $q$

Part 6) $p\geq -121/13$

Step-by-step explanation:      

Part 1)  $-r^{3}\leq 6$          

Multiply by -1 both sides

$r^{3}\geq -6$    

$r\geq \sqrt[3]{-6}$

$r\geq -1.817$

The solution is the interval -------> [-1.817,∞)

The solution in the attached figure N 1    

Part 2)  $-4>-43s$    

rewrite

$-43s$      

Multiply by -1 both sides

 $43s>4$    

 $s>4/43$      

 $s>0.09$    

The solution is the interval--------> (0.09,∞)

The solution in the attached figure N 2

Part 3) $z-2-6\leq-2$

combine like terms

$z-8\leq-2$  

Adds 8 both sides

$z\leq-2+8$

$z\leq6$

The solution is the interval--------> (-∞,6]

The solution in the attached figure N 3  

Part 4) $-2t-5$    

Adds 5 both sides

$-2t$

$-2t$

Multiply by -1 both sides

$2t>-14$

Divide by 2 both sides

$t>-7$

The solution is the interval--------> (-7,∞)

The solution in the attached figure N 4  

Part 5) $7(q+2)$

applying distributive property left side

$7q+14$

Subtract 14 both sides

$7q$

$7q$

Divide by 7 both sides

$q$

$q$

The solution is the interval--------> (-∞,-13)

The solution in the attached figure N 5

Part 6) $-13(p+9)\leq4$

applying distributive property left side

$-13p-117\leq4$

Adds 117 both sides

$-13p\leq4+117$

$-13p\leq 121$

Divide by -1 both sides

$13p\geq -121$

Divide by 13 both sides

$p\geq -121/13$

$p\geq -9.31$

The solution is the interval--------> [-9.31,∞)  

The solution in the attached figure N 5