Let's solve each equation involving absolute value:

(a) $|m| = 3$

The absolute value of a number represents its distance from zero on the number line, regardless of direction. So, for $|m| = 3$, there are two possible solutions:

• $m = 3$ (positive direction)
• $m = -3$ (negative direction)

Thus, the solutions are: $m = 3, -3$

(b) $|m| = 0$

The absolute value of a number is only 0 if the number itself is 0. So, for $|m| = 0$, the only solution is: $m = 0$

(c) $|m| = -6$

The absolute value of any real number is always non-negative (i.e., it can never be negative). Therefore, there are no solutions to the equation $|m| = -6$.

So, for this case, there is no solution.

Summary of the solutions:

• (a) $m = 3, -3$
• (b) $m = 0$
• (c) No solution

Would you like to go over how absolute value works in more detail, or do you have any other questions?

Here are some related questions for further exploration:

1. What is the general rule for solving equations of the form $|m| = a$, where $a > 0$?
2. How do you handle absolute value equations with multiple terms, such as $|m + 2| = 4$?
3. What happens when you have an absolute value inequality, like $|m| \leq 3$?
4. How does absolute value work in complex numbers, e.g., $|3 + 4i|$?
5. What are the key properties of absolute value that make it useful in solving equations?

Tip: Remember, the absolute value $|m| = a$ always gives two possible solutions when $a > 0$, namely $m = a$ and $m = -a$.