Answer
$(0.9996, 1.0004)$
Work Step by Step
Step 1. Based on the given conditions, we have $|y-6|\lt0.002$
Step 2. Use $y=5x+1$, we have $|5x+1-6|\lt0.002$ or $|5x-5|\lt0.002$
Step 3. The above is equivalent to $-0.002\lt 5x-5 \lt 0.002$ or $4.998\lt 5x \lt 5.002$
Step 4. We have the answer as $0.9996\lt x \lt 1.0004$ or $x\in (0.9996, 1.0004)$
