Question

On your basketball team, the starting players' scoring averages are between 8 and 22 points per game. Write an absolute-value inequality describing the scoring averages for the players.

Short answer

The absolute-value inequality describing the scoring averages for the players is \( |x - 15| \leq 7 \)

Step-by-step solution

Determine the center point

To establish an absolute-value inequality, the center point is required. This is calculated by finding the average between the maximum and minimum values. For a scoring range of 8 to 22, the average would be \( (8+22)/2 = 15 \). Thus, 15 is the center point.

Calculate the distance from the center

Next, determine the distance between the center point and either limit of the range. The distance can be calculated as the absolute difference between the center point and either the upper or lower limit of the range. Here, you can choose 22 or 8. For instance, choosing 22, the calculation is \( |22 - 15| = 7 \). So, 7 is the distance from the center to the points described.

Write the absolute value inequality

Combine the center point and distance to write the inequality describing the scoring averages. It is an absolute value inequality of the form \( |x - a| \leq b \), where \( x \) represents the players' scoring averages, \( a \) is the center point, and \( b \) is the distance. Substituting the values, the inequality is \( |x - 15| \leq 7 \). This inequality implies that the players' scoring averages could be 7 points above or below the average of 15.