Chapter R - Algebra Reference - R.5 Inequalities - R.5 Exercises - Page R-21: 34

$10r^2+r\leq2$ $10r^2+r-2\leq0$ $(5r-2)(2r+1)\leq0$ $\frac{-1}{2}\leq r \leq\frac{2}{5}$

Step 1: Subtract 2 from both sides of the inequality Step 2: Factorize trinomial inequality Step 3: The quadratic inequality is smaller than and equal to $0$ for $\frac{-1}{2}\leq r \leq\frac{2}{5}$