## Precalculus (6th Edition) Blitzer

$[-1, -\displaystyle \frac{1}{5}].$
"$y$ is at least $6$" $\qquad$ is written as $\quad y\geq 6.$ Substituting the expression for y, $8-|5x+3|\geq 6\qquad$ ... add $+|5x+3|-6$ $2\geq|5x+3|\qquad$ ... rewrite (exchange sides, preserve direction) $|5x+3|\leq 2$ ... $|u| \leq c$ is equivalent to $\quad -c \leq u \leq c.$ $-2\leq 5x+3\leq 2\qquad$ ... add $(-3)$ $-5\leq 5x\leq-1\qquad$ ... multiply with $(\displaystyle \frac{1}{5})$ $-1\displaystyle \leq x\leq-\frac{1}{5}$ Borders are included: Solution set: $[-1, -\displaystyle \frac{1}{5}].$