Chapter 1 - Section 1.8 - Absolute Value Equations and Inequalities - 1.8 Exercises - Page 155: 89

$0.9996\leq x\leq 1.0004$

First, set the inequality: $$|y-6|\leq0.002$$ Substitute value of $y$: $$|5x+1-6|\leq0.002$$ $$|5x-5|\leq0.002$$ Removing absolute value as: $$-0.002\leq 5x-5\leq 0.002$$ Solve for $x$: $$-0.002+5\leq 5x\leq 0.002+5$$ $$4.998\leq 5x\leq 5.002$$ $$\frac{4.998}{5}\leq x\leq \frac{5.002}{5}$$ $$0.9996\leq x\leq 1.0004$$