We are given the inequality:

$-3|s| < -12$

Step 1: Isolate the Absolute Value Expression

First, divide both sides by $-3$. Since we are dividing by a negative number, we must reverse the inequality sign:

$|s| > 4$

Step 2: Convert to a Compound Inequality

The absolute value inequality $|s| > 4$ means that $s$ is either greater than 4 or less than -4. This results in the compound inequality:

$s < -4 \quad \text{or} \quad s > 4$

Final Answer:

$s < -4 \quad \text{or} \quad s > 4$

Would you like a step-by-step explanation with examples?

Related Questions:

1. Solve $2|x| - 5 > 7$ and write the answer as a compound inequality.
2. Solve $-4|y| \leq -8$ and express the solution in interval notation.
3. What does it mean graphically when solving absolute value inequalities?
4. Solve $|m + 2| < 5$ and express the solution as an inequality.
5. How do you solve $|k - 3| \geq 6$ and write the answer in set notation?

Tip:

When solving absolute value inequalities, always remember:

• $|x| < a$ means $-a < x < a$
• $|x| > a$ means $x < -a$ or $x > a$