Question

Which of the following inequalities has no solution?

Answer 1

Solving all the 4 choices would show us the right answer.

Number 1:

`-4m-10\leq -22\\-4m\leq -12\\m\geq 3` (Note: that multiplying/dividing by a negative number reverses the inequality sign)

`6m-8\geq 22\\6m\geq 30\\m\geq 5`

The first one says m is greater than or equal to 3 and second one says m is greater than or equal to 5. So there are solutions that overlap and satisfies both.

Number 2:

`-6m\geq 12\\m\leq -2`

`m+5<7\\m<2`

The first one says m is less than or equal to -2 and second one says m is less than 2. So there are solutions that overlap and satisfies both.

Number 3:

`-5m<20\\m>-4`

`6m>-18\\m>-3`

The first one says m is greater than -4 and second one says m is greater than -3. So there are solutions that overlap and satisfies both.

Number 4:

`3m-12>30\\3m>42\\m>14`

`-6m\geq 24\\m\leq -4`

The first one says m is greater than 14 and second one says m is less than or equal to -4. There is NO number that is both greater than 14 AND less than -4.

So, the fourth option doesn't have solution.

ANSWER: Inequalities
`3m-12>30` and
`-6m\geq 24` (option 4) doesn't have a solution.