We are given the inequality:

$|4m - 4| < 36$

To solve this absolute value inequality, we can follow these steps:

Step 1: Remove the absolute value

The absolute value inequality $|4m - 4| < 36$ means that:

$-36 < 4m - 4 < 36$

Step 2: Solve the inequality for $m$

First, add 4 to all parts of the inequality:

$-36 + 4 < 4m < 36 + 4$

$-32 < 4m < 40$

Now, divide the entire inequality by 4:

$\frac{-32}{4} < m < \frac{40}{4}$

$-8 < m < 10$

Final solution:

The solution to the inequality is:

$m \in (-8, 10)$

This means $m$ must lie between $-8$ and $10$, not including the endpoints.

Would you like more details or have any other questions?

Here are five related questions for practice:

1. Solve $|2x + 3| < 7$.
2. Solve $|5y - 2| > 10$.
3. Solve $|3p + 1| \leq 12$.
4. Solve $|7z - 8| \geq 14$.
5. Solve $|6k - 5| = 15$.

Tip: When solving absolute value inequalities, always consider breaking them into two separate inequalities depending on the sign (positive and negative).