Solving all the 4 choices would show us the right answer.
Number 1:
[tex]-4m-10\leq -22\\-4m\leq -12\\m\geq 3[/tex] (Note: that multiplying/dividing by a negative number reverses the inequality sign)
[tex]6m-8\geq 22\\6m\geq 30\\m\geq 5[/tex]
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:
[tex]-6m\geq 12\\m\leq -2[/tex]
[tex]m+5<7\\m<2[/tex]
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:
[tex]-5m<20\\m>-4[/tex]
[tex]6m>-18\\m>-3[/tex]
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:
[tex]3m-12>30\\3m>42\\m>14[/tex]
[tex]-6m\geq 24\\m\leq -4[/tex]
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 [tex]3m-12>30[/tex] and [tex]-6m\geq 24[/tex] (option 4) doesn't have a solution.
