Find all solutions to the inequality \[\frac{1}{2} \le \frac{x+1}{x} \le \frac{3}{2}.\]
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Find all solutions to the inequality \[\frac{1}{2} \le \frac{x+1}{x} \le \frac{3}{2}.\]
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
(-\infty, -2] \cup [2, \infty)
Find all solutions to the inequality \[\frac{1}{2} \le \frac{x+1}{x} \le \frac{3}{2}.\]
train