Question

Which inequality has –12 in its solution set?

A.x+6<-8 B.x+4>=-6 C.x-3>-10 D.x+5<=-4

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

Option D.

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.