Question

Diana is aiming for a college grade point average (GPA) between 3.5 and 3.8 to remain on the dean’s list. If g represents Diana’s GPA, which of the following absolute value inequalities represents the possible GPAs Diana can earn in order to remain on the dean’s list?(1 point)
Responses

|g−0.15|≤3.65
Start Absolute Value g minus 0.15 End Absolute Value less-than-or-equal-to 3.65

|g−3.65|>0.15
Start Absolute Value g minus 3.65 End Absolute Value greater than 0.15

|g−0.15|>3.65
Start Absolute Value g minus 0.15 End Absolute Value greater than 3.65

|g−3.65|≤0.15

Answer 1

To determine the appropriate absolute value inequality for Diana's GPA, we first need to find the range of GPAs she wants to achieve, which is between 3.5 and 3.8.

The midpoint of this range is:
\[
\frac{3.5 + 3.8}{2} = \frac{7.3}{2} = 3.65
\]
The distance from this midpoint to the lower and upper limits can be calculated as:
\[
3.65 - 3.5 = 0.15 \quad \text{(distance to lower limit)}
\]
\[
3.8 - 3.65 = 0.15 \quad \text{(distance to upper limit)}
\]

Thus, the GPA \( g \) can be written in terms of its distance from the midpoint 3.65. The equivalent absolute value inequality describing the range of GPAs that Diana can earn to remain on the dean’s list is:
\[
|g - 3.65| \leq 0.15
\]

This means that her GPA \( g \) can deviate from 3.65 by at most 0.15, which results in the range of 3.5 to 3.8.

Therefore, the correct response is:
\[
|g - 3.65| \leq 0.15
\]