Answer:
[tex]x < -2[/tex].
Step-by-step explanation:
It is given that [tex]3x + 6 < 12[/tex] and [tex]6x + 24 < 12[/tex].
For [tex]3x + 6 < 12[/tex],
[tex]3x < 12-6[/tex]
[tex]3x < 6[/tex]
Divide both sides by 2.
[tex]x < 2[/tex] ...(i)
For [tex]6x + 24 < 12[/tex],
[tex]6x< 12-24[/tex]
[tex]6x< -12[/tex]
Divide both sides by 6.
[tex]x < -2[/tex] ...(ii)
From (i) and (ii), we get
[tex]x < 2\text{ and }x<-2[/tex]
[tex]\Rightarrow x<-2[/tex]
Therefore, the required answer is [tex]x < -2[/tex].
