Answer:No solution Step-by-step explanation:Given: [tex]12x+7<-11[/tex] and [tex]5x-8\geq 40[/tex]Solve both inequality separately. [tex]12x+7<-11[/tex] Subtraction property of inequality [tex]12x<-11-7[/tex][tex]12x<-18[/tex][tex]x<-\dfrac{18}{12}[/tex][tex]x<-\dfrac{3}{2}[/tex]and [tex]5x-8\geq 40[/tex] Addition property of inequality [tex]5x\geq 40+8[/tex][tex]5x\geq 48[/tex][tex]x\geq \dfrac{48}{5}[/tex]Hence, the solution of the compound inequality intersection of both solutions. Please find attachment for number line solution.No solution