To solve the inequality $-4|y| + 2 \leq -10$, let's proceed step by step:

Step 1: Subtract 2 from both sides

$-4|y| \leq -12$

Step 2: Divide both sides by $-4$

Since we're dividing by a negative number, we must reverse the inequality: $|y| \geq 3$

Step 3: Solve the absolute value inequality

The absolute value inequality $|y| \geq 3$ means that $y$ can be either greater than or equal to 3 or less than or equal to $-3$: $y \geq 3 \quad \text{or} \quad y \leq -3$

Final Answer:

The solution to the inequality is: $y \geq 3 \quad \text{or} \quad y \leq -3$

Would you like a deeper explanation or have any questions?

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Here are 5 related questions for further practice:

1. Solve the inequality $-3|x| + 5 \leq -4$.
2. What is the solution to $|y| + 2 \geq 5$?
3. How would you solve $-5|x| + 1 < -9$?
4. Solve the inequality $|y| - 7 \leq 1$.
5. Solve $-2|x| + 3 \geq -1$.

Tip: Remember, when dividing or multiplying both sides of an inequality by a negative number, always reverse the direction of the inequality sign!