Question

Which inequality has –12 in its solution set?

Answer 1

-12 = x+5<=-4 -12+5=-7 so -7<-4 So the conclusion is that negative seven is less than negative four.

Answer 2

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,

$x+6$

Subtract 6 from both sides.

$x+6-6$

$x$

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.