#### Answer

$[-4,\infty)$

#### Work Step by Step

Step 1: $-2x+8\leq16$
Step 2: Subtracting $8$ from both sides, $-2x+8-8\leq16-8$
Step 3: $-2x\leq8$
Step 4: Dividing both sides by -2 (this reverses the direction of the inequality symbol):
$\frac{-2x}{-2} \geq \frac{8}{-2}$
Step 5: $x\geq-4$
According to the inequality, the interval includes $-4$ and all values greater than $-4$. Since $-4$ is part of the interval, a square bracket is used on its side. On the other hand, $\infty$ does not represent an actual number. Rather it is used to show that the interval includes all real numbers greater than -4. Therefore, a parenthesis is used on its side.
Therefore, the interval notation for this inequality is written as $[-4,\infty)$.