What are the possible values for A in the inequality where the absolute value of 4A is greater than 72?

To analyze the inequality given by the absolute value of 4A being greater than 72, we can write this mathematically as |4A| > 72.

Absolute value inequalities can be split into two separate cases:

1. (4A > 72)

2. (4A < -72)

For the first case, (4A > 72), dividing both sides by 4 gives:

[A > \frac{72}{4} = 18]

For the second case, (4A < -72), again dividing both sides by 4 results in:

[A < \frac{-72}{4} = -18]

Thus, the combined solutions to the inequality |4A| > 72 are:

• A is greater than 18, or

• A is less than -18.

This perfectly matches the correct choice, indicating the range of values for A that satisfy the inequality. Therefore, the solution set is A is greater than 18 or A is less than negative 18. The definition and properties of absolute values provide a solid foundation for this interpretation of the inequality.