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.
$$-8x+3>-5\text{ OR }-2x-4\le -12$$

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

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 $-2x-4\le -12$. Add 4 to both sides to get $-2x\le -8$. Divide both sides by -2 to get $x\ge 4$. Again, remember to flip the inequality sign.

Step 4 ：The solution to the compound inequality is $x<1$ OR $x\ge 4$. 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 $(-\mathrm{\infty },1)\cup [4,\mathrm{\infty })$.

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