solution: Getting rid of the absolute value, we have $-5.6 \le x-2 \le 5.6$, or $-3.6 \le x \le 7.6$. Thus, $x$ can be any integer from -3 to 7, inclusive. There are $7-(-3)+1=\boxed{11}$ integers in this range.
prompt.content: <|im_start|>system
  You are a helpful assistant.<|im_end|>
  <|im_start|>user
  How many integers are in the solution set of $|x-2|\leq5.6$ ?
  Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
  <|im_start|>assistant
  
prompt.role: user
extra_info.answer: 11
extra_info.question: How many integers are in the solution set of $|x-2|\leq5.6$ ?
extra_info.split: test