Answer
$[8.59,8.61]$
Work Step by Step
Consider the inequality $|x-8.6|\leq 0.01$
or, $x \leq 0.01+8.6$
This implies that $x \leq 8.61$
Now, $|x-8.6|\leq 0.01$
or, $x \geq -0.01+8.6$
This implies that $x \geq 8.59$
or, $8.59 \leq x \leq 8.61$
Hence, $[8.59,8.61]$
