He should place the picture at 6.75 inches from the edge of the wall.
Explanation
According to the below diagram, O is the center of the wall and AB is the distance of the picture from the edge of the wall.
As the length of the wall is [tex]31\frac{3}{4}[/tex] inches or 31.75 inches , so the half length of the wall [tex](OB)[/tex] [tex]=\frac{31.75}{2}=15.875[/tex] inches.
Now, the length of the picture is [tex]18\frac{1}{4}[/tex] inches or 18.25 inches, so the half length of the picture [tex](OA)[/tex] [tex]= \frac{18.25}{2}=9.125[/tex] inches.
Thus, [tex]AB= OB-OA= 15.875-9.125=6.75[/tex] inches
So, he should place the picture at 6.75 inches from the edge of the wall.
