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,
\(x+6<-8\)
Subtract 6 from both sides.
\(x+6-6<-8-6\)
\(x<-14\)
Since -12>-14, therefore -12 is not included in the solution set of x+6<-8.
Option B,
\(x+4\geq -6\)
Subtract 4 from both sides.
\(x+4-4\geq -6-4\)
\(x\geq -10\)
Since -12<-10, therefore -12 is not included in the solution set of \(x+4\geq -6\).
Option C,
\(x-3>-10\)
Add 3 on both sides.
\(x-3+3>-10+3\)
\(x>-7\)
Since -12<-7, therefore -12 is not included in the solution set of x-3>-10.
Option D,
\(x+5\leq -4\)
Subtract 5 from both sides.
\(x+5-5\leq -4-5\)
\(x\leq -9\)
Since -12<-9, therefore -12 is included in the solution set of \(x+5\leq -4\).
Therefore, the correct option is D.
