Answer :

To solve the equation [tex]\( A = \frac{e+f}{2} \)[/tex] for [tex]\( e \)[/tex], follow these detailed steps:

1. Start with the given equation:
[tex]\[ A = \frac{e + f}{2} \][/tex]

2. Eliminate the fraction by multiplying both sides of the equation by 2:
[tex]\[ 2A = e + f \][/tex]

3. Isolate the variable [tex]\( e \)[/tex] by subtracting [tex]\( f \)[/tex] from both sides of the equation:
[tex]\[ 2A - f = e \][/tex]

4. Therefore, the solution for [tex]\( e \)[/tex] is:
[tex]\[ e = 2A - f \][/tex]

Thus, the expression for [tex]\( e \)[/tex] in terms of [tex]\( A \)[/tex] and [tex]\( f \)[/tex] is:
[tex]\[ e = 2A - f \][/tex]