#### Answer

{-14}.

#### Work Step by Step

x-3= -17
Step 1: Add 3 on both the sides
x-3+3 = -17+3
Step 2: Simplify
x= -14
Now we check the proposed solution, -14, by replacing x with -14 in the original equation.
Step 1: the original equation x-3 =-17
Step2: Substitute -14 for x
-14 - 3 = -17
Step 3: Add -14 - 7 = -17
-17 = -17
Since the check results in true statement, we conclude that the solution set of the given equation is {-14}.