To solve for x, we can use the following steps:

1. Multiply both sides of the equation by 11 to eliminate the denominator:

(x-37):11 * 11 = 47 * 11

This simplifies to:

x - 37 = 517

2. Add 37 to both sides of the equation to isolate x:

x - 37 + 37 = 517 + 37

This simplifies to:

x = 554

Therefore, the solution to the equation (x-37):11=47 is x = 554.