Graph the inequality and give interval notation for the solution. Use two o's (as in octopus) for inifinity and a $\mathrm{U}$ for union as needed.
\[
-8 x+3> -5 \text { OR }-2 x-4 \leq-12
\]

Step 1 ：Solve the compound inequality: \(-8x + 3 > -5\) OR \(-2x - 4 \leq -12\).

Step 2 ：First, solve the inequality \(-8x + 3 > -5\). Add -3 to both sides to get \(-8x > -8\). Divide both sides by -8 to get \(x < 1\). Remember that when you divide or multiply by a negative number, you must flip the inequality sign.

Step 3 ：Next, solve the inequality \(-2x - 4 \leq -12\). Add 4 to both sides to get \(-2x \leq -8\). Divide both sides by -2 to get \(x \geq 4\). Again, remember to flip the inequality sign.

Step 4 ：The solution to the compound inequality is \(x < 1\) OR \(x \geq 4\). This means that x is less than 1 or x is greater than or equal to 4.

Step 5 ：In interval notation, this is written as \((-\infty, 1) \cup [4, \infty)\).

Step 6 ：\(\boxed{(-\infty, 1) \cup [4, \infty)}\) is the final answer.