Answer:
Option D. [tex]x+5\leq -4[/tex]
Step-by-step explanation:
Verify each case
case A) we have
[tex]x+6< -8[/tex]
Solve for x
Subtract 6 both sides
[tex]x< -8-6[/tex]
[tex]x< -14[/tex]
The solution is the interval -----> (-∞,-14)
therefore
This inequality does not have -12 in its solution
case B) we have
[tex]x+4\geq -6[/tex]
Solve for x
Subtract 4 both sides
[tex]x\geq -6-4[/tex]
[tex]x\geq -10[/tex]
The solution is the interval -----> (-10,∞)
therefore
This inequality does not have -12 in its solution
case C) we have
[tex]x-3 > -10[/tex]
Solve for x
Adds 3 both sides
[tex]x > -10+3[/tex]
[tex]x > -7[/tex]
The solution is the interval -----> (-7,∞)
therefore
This inequality does not have -12 in its solution
case D) we have
[tex]x+5\leq -4[/tex]
Solve for x
Subtract 5 both sides
[tex]x\leq -4-5[/tex]
[tex]x\leq -9[/tex]
The solution is the interval -----> (-∞,-9)
therefore
This inequality has -12 in its solution
