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

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

• A. A is greater than 18 or A is less than negative 18
• B. A is between negative 18 and 18
• C. A is greater than negative 72 or A is less than 72
• D. A is equal to zero

Answer: (A)

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.

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.