#### Answer

$[-1, \frac{-1}{5}]$

#### Work Step by Step

Plug the given conditions into an inequality. Solve the first inequality by removing the absolute value sign and simplifying, and solve the second inequality by flipping the sign, making the right side negative, and then simplifying.
$8-|5x+3|\geq6$
$-|5x+3|\geq-2$
$|5x+3|\leq2$
$5x+3\leq2$
$5x\leq-1$
$x\leq\frac{-1}{5}$
$5x+3\geq-2$
$5x\geq-5$
$x\geq-1$
$-1\leq x\leq\frac{-1}{5}$
$[-1, \frac{-1}{5}]$