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!

Learn how to solve the inequality –4|y| + 2 ≤ –10 step by step. This solution involves understanding absolute value inequalities and the key rule of reversing inequalities when dividing by a negative number. Suitable for students in Grades 8-10.

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