Chapter 1 - Equations and Inequalities - 1.8 Absolute Value Equations and Inequalities - 1.8 Exercises - Page 168: 76

$(0.3998,0.4002)$

Step 1. Based on the given conditions, we have $|y-6|\lt0.002$ Step 2. Use $y=10x+2$, we have $|10x+2-6|\lt0.002$ or $|10x-4|\lt0.002$ Step 3. The above is equivalent to $-0.002\lt 10x-4 \lt 0.002$ or $3.998\lt 10x \lt 4.002$ Step 4. We have the answer as $0.3998\lt x \lt 0.4002$ or $x\in (0.3998,0.4002)$