Answer:
Option D.
Step-by-step explanation:
We need to find an inequality that has –12 in its solution set.
Solve each of the given inequalities.
Option A,
[tex]x+6<-8[/tex]
Subtract 6 from both sides.
[tex]x+6-6<-8-6[/tex]
[tex]x<-14[/tex]
Since -12>-14, therefore -12 is not included in the solution set of x+6<-8.
Option B,
[tex]x+4\geq -6[/tex]
Subtract 4 from both sides.
[tex]x+4-4\geq -6-4[/tex]
[tex]x\geq -10[/tex]
Since -12<-10, therefore -12 is not included in the solution set of [tex]x+4\geq -6[/tex].
Option C,
[tex]x-3>-10[/tex]
Add 3 on both sides.
[tex]x-3+3>-10+3[/tex]
[tex]x>-7[/tex]
Since -12<-7, therefore -12 is not included in the solution set of x-3>-10.
Option D,
[tex]x+5\leq -4[/tex]
Subtract 5 from both sides.
[tex]x+5-5\leq -4-5[/tex]
[tex]x\leq -9[/tex]
Since -12<-9, therefore -12 is included in the solution set of [tex]x+5\leq -4[/tex].
Therefore, the correct option is D.
