Chapter 1 - Section 1.8 - Absolute Value Equations and Inequalities - 1.8 Exercises - Page 155: 90

$0.3998\leq x\leq 0.4002$

First, set the inequality: $$|y-6|\leq0.002$$ Substitute value of $y$: $$|10x+2-6|\leq0.002$$ $$|10x-4|\leq0.002$$ Removing absolute value as: $$-0.002\leq 10x-4\leq 0.002$$ Solve for $x$: $$-0.002+4\leq 10x\leq 0.002+4$$ $$3.998\leq 10x\leq 4.002$$ $$\frac{3.998}{10}\leq x\leq \frac{4.002}{10}$$ $$0.3998\leq x\leq 0.4002$$