Answer:
The correct option is 1.
Step-by-step explanation:
On solving both equations of option 1.
[tex]4m\leq -32[/tex]
[tex]m\leq -8[/tex]
From first equation the value of m is less than or equal to -8.
[tex]m+28>23[/tex]
[tex]m>-5[/tex]
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
[tex]3m+2\geq 2[/tex]
[tex]m\geq 0[/tex]
[tex]-3m+5\leq -10[/tex]
[tex]-3m\leq -15[/tex]
Divide both sides by -3. When we divide the inequality by a negative number, then we have to change the sign of inequality.
[tex]m\geq 5[/tex]
Since m is greater than or equal to 0 and 5, therefore option 2 have common solution [tex]m\geq 5[/tex]. So, the second option is incorrect.
On solving equation both equations of option 3, we get
[tex]-2m< 2[/tex]
[tex]m>-1[/tex]
[tex]11m>22[/tex]
[tex]m>2[/tex]
Since m is greater than -1 and 2, therefore option 3 have common solution [tex]m>2[/tex]. So, the third option is incorrect.
On solving equation both equations of option 4, we get
[tex]m+12< 8[/tex]
[tex]m<-4[/tex]
[tex]-2m\leq 6[/tex]
[tex]m\leq -3[/tex]
Since m is less than -4 and less than or equal to -3, therefore option 4 have common solution [tex]m<-4[/tex]. So, the fourth option is incorrect.
