Question

A hole needs to be at least 40 feet below ground level. This means it needs to be more than 2 1/2 times it’s current depth. This depth is represented by the inequality 2 1/2d < -40, where d is the current depth of the hole. Select from the drop-down to correctly interpret the solution of this inequality.

The current depth of the hole is feet below ground level.
A.) The current depth of the hole is at most 16 feet below ground
B.) The current depth of the hole is deeper than 16 feet below ground
C.) The current depth of the hole is less than 16 feet below ground level

Answer 1

The correct interpretation of the inequality 2 1/2d < -40 is that the current depth of the hole is deeper than 16 feet below ground level (option B).

Step-by-step explanation:

The inequality representing the current depth of the hole is 2 1/2d < -40. To solve this inequality for the current depth d, we first convert the mixed number to an improper fraction, which gives us 5/2d < -40. We then multiply both sides of the inequality by the reciprocal of 5/2, which is 2/5, to isolate d.

This step gives us d < -16. Since depth below ground level is a positive number, the inequality indicates that the current depth is greater than 16 feet, but since we're dealing with negative values to represent depth below ground, the option B is the correct interpretation.