Question

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

Answer 1

The correct option is 1.

Explanation:

On solving both equations of option 1.

`4m\leq -32`

`m\leq -8`

From first equation the value of m is less than or equal to -8.

`m+28>23`

`m>-5`

From second equation the value of m is greater than -5. Therefore option have no common solutions.

On solving equation both equations of option 2, we get

`3m+2\geq 2`

`m\geq 0`

`-3m+5\leq -10`

`-3m\leq -15`

Divide both sides by -3. When we divide the inequality by a negative number, then we have to change the sign of inequality.

`m\geq 5`

Since m is greater than or equal to 0 and 5, therefore option 2 have common solution
`m\geq 5`. So, the second option is incorrect.

On solving equation both equations of option 3, we get

`-2m< 2`

`m>-1`

`11m>22`

`m>2`

Since m is greater than -1 and 2, therefore option 3 have common solution
`m>2`. So, the third option is incorrect.

On solving equation both equations of option 4, we get

`m+12< 8`

`m<-4`

`-2m\leq 6`

`m\leq -3`

Since m is less than -4 and less than or equal to -3, therefore option 4 have common solution
`m<-4`. So, the fourth option is incorrect.