The total number of seats in a movie theater is calculated by adding the area of the upper section given by 8x2 and the area of the lower section given by 6x2. the theater plans to add an addition of front row seats given by 4x for a total of 138 seats. which equation could be used to solve for the number of seats in the front row addition?

First, let's assume that the numbers given corresponds to the length and width of the area. 

*area = l x w*
a1 (upper area) = 8 x 2
a2 (lower area) = 6 x 2
a3 (front row) = 4 x ?

It's logical to say the a3 should have 2 as it's width. By this, we can now calculate the total length and width. For these 3 given, we can say that the total length is 18 (8 + 6 + 4) and we can get the percentage per location and we can described later how many seats it represent from the total of 138.

a1 = 8 ÷ 18 X 100
a1 = 44.44%

a2 = 6 ÷ 18 X 100
a2 = 33.33%

a3 = 4 ÷ 18 X 100
a3 = 22.22%

We now know the percentages that each area represents, so we can used these to solve for the number of seats.

a1 = 138 x 0.44
a1 = 61 seats

a2 = 138 x 0.33
a2 = 46 seats

a3 = 138 x 0.22
a3 = 31 seats

To check, we can add 61 seats + 46 seats + 31 seats, and we will get a total of 138 seats.