Answer
$[-1, -\displaystyle \frac{1}{5}].$
Work Step by Step
"$ 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: $[-1, -\displaystyle \frac{1}{5}].$
