Final answer:
To solve the system of inequalities 4x-39>-43 and 8x+31<23, we isolate x in both equations. The solution to the system of inequalities is x>-1 or x<-1.875, but since the second inequality contradicts the first one, there are no solutions.
Step-by-step explanation:
To solve the inequalities 4x-39>-43 and 8x+31<23, we need to isolate x in both equations.
For the first equation, we add 39 to both sides and then divide by 4 to get x>-1.
For the second equation, we subtract 31 from both sides and then divide by 8 to get x<-1.875.
Therefore, the solution to the system of inequalities is x>-1 or x<-1.875, but since the second inequality contradicts the first one, there are no solutions.