Answer
$x\geq6$ or $x\leq4$.
Work Step by Step
$|x-5|\geq1$ implies $x-5\geq1\\x\geq6$ or $x-5\leq-1\\x\leq4$.
Thus $x\geq6$ or $x\leq4$.
Then, by using a graphing utility, the solution set is attached.
![](https://gradesaver.s3.amazonaws.com/uploads/solution/875d0777-9411-4128-a7f7-7b1a7b05faae/steps_image/small_1573037350.png?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T020713Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=0c2d35ce6e7e5822da66ad46beb51a2d117b5b8ec5e9353b67737b84e7fe7624)
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