Answer :
Final answer:
The absolute value equation representing the minimum and maximum distances between Earth and Venus as solutions is |d - 149.6| = 111.4, where d is the distance in million kilometers.
Explanation:
To determine an absolute value equation that has the minimum and maximum distances between Earth and Venus as its solutions, we first consider the average of these two distances. The average distance would be the midpoint between the minimum and maximum, so we calculate (38.2 million km + 261 million km) / 2, which equals 149.6 million kilometers. This average distance will be the distance from which variations (either positive or negative) equal to half the range between the maximum and minimum distances can occur to reach either distance from the average.
Half the range is calculated by (261 million km - 38.2 million km) / 2, which equals 111.4 million kilometers. Therefore, the absolute value equation with the average distance as the mid-point and the half range as the distance that can vary in either direction will have the standard form |d - 149.6| = 111.4, where d represents the distance from Earth to Venus in million kilometers.
The absolute value equation that has the minimum and maximum distances between Earth and Venus as its solutions is |d - 149.6| = 111.4.
