Question

For which of the following compound inequalities is there no solution?

A. 3m - 12 > 30 and -6m >= 24
B. -6m >= 12 and m + 5 -18
C. -5m < 20 and 6m > -18
D. -4m - 10 <= -22 and 6m - 8 >= 22
>= is greater than or equal to
<= is less than or equal to

Answer 1

3m - 12 > 30 and -6m >= 24

Explanation:

A. 3m - 12 > 30 and -6m >= 24

3m > 42 and m < = -4

m > 14 and m < = -4

This has no solution

B. -6m >= 12 and m + 5 -18

cannot solve since missing inequality

C. -5m < 20 and 6m > -18

m > -4 and m > -3

solution m > -3

D. -4m - 10 <= -22 and 6m - 8 >= 22

-4m < = -12 and 6m > = 30

m > = 3 and m > =5

m > = 5

Answer 2

A

Explanation:

`3m - 12 > 30 \text{ and } -6m\geq 24`

`\boxed{3m - 12 > 30 \wedge -6m\geq 24}`

`m>14 \wedge m\leq -4`

There's no solution. It is the first one already. There is no number that is both greater than 14 and less than or equal to -4. That is no solution because there's no
`m` that satisfy the compound inequality.

Note: the signal change because we divided by negative number.