Chapter 11 - Additional Topics - 11.1 - Equations and Inequalities Involving Absolute Value - Problem Set 11.1 - Page 475: 33

{$-6,\frac{16}{3}$}

Using the rules for absolute values to generate two equations, we obtain: Step 1: $|-3x-1|=17$ Step 2: $-3x-1=17$ and $-3x-1=-17$ Step 3: $-3x=17+1$ and $-3x=-17+1$ Step 4: $-3x=18$ and $-3x=-16$ Step 5: $x=\frac{18}{-3}$ and $x=\frac{-16}{-3}$ Step 6: $x=-6$ and $x=\frac{16}{3}$ Therefore, the solution set for the equation is {$-6,\frac{16}{3}$}.