Final answer:
The absolute value equation that represents the range of free throws attempted by James Harden with solutions equal to the maximum and minimum attempts is |attempts - x| = 14. To find the average, we solve for x considering that the actual average is the midpoint between the smallest and the largest number of attempts, which leads to James Harden averaging 11 free throw attempts per game.
Step-by-step explanation:
To create an absolute value equation that has solutions equal to the minimum (3) and maximum (25) free throws attempted by James Harden, consider how absolute value equations work. They measure the distance of a number from zero on the number line, so we need an equation that represents a distance of 3 and 25 from the average number of free throws. Let's call the average number of free throw attempts per game x.The absolute value of the difference between the number of attempts in a game and the average is equal to the value halfway between 3 and 25. That midpoint is (3+25)/2 = 14. The equation will therefore be:To write an absolute value equation with solutions equal to the minimum and maximum of free throws attempted by James Harden, we can let x represent the number of free throws attempted.
The equation would be |x - 3| = 25, since the minimum number of attempts is 3 and the maximum is 25. Solving this equation would give us x = 3 and x = 28 as the solutions.To find the average number of free throw attempts per game, we can add up all the attempts and divide by the number of games played. Without knowing the number of games, we cannot determine the exact average attempts per game.|attempts - x| = 14This equation indicates that the number of attempts may be either 14 more or 14 less than the average, x, which leads to two potential solutions for the number of attempts: x + 14 = 25 and x - 14 = 3. Solving these gives:x + 14 = 25 x = 25 - 14x = 11And for the other equation:x - 14 = 3 x = 3 + 14 x = 17However, since the average cannot be two different numbers, the correct average is the solution that's the midpoint between the maximum and minimum values, which is 11. Hence, James Harden averages 11 free throw attempts per game.