Solve the following equation for [tex]$a$[/tex]. Be sure to take into account whether a letter is capitalized or not.

[tex] d^2 = \frac{1}{3}a - f [/tex]



Answer :

To solve the equation [tex]\( d^2 = \frac{1}{3} a - f \)[/tex] for [tex]\( a \)[/tex], follow these steps:

1. Start with the given equation:
[tex]\[ d^2 = \frac{1}{3} a - f \][/tex]

2. Isolate [tex]\( \frac{1}{3} a \)[/tex] on one side of the equation:
[tex]\[ d^2 + f = \frac{1}{3} a \][/tex]

3. Clear the fraction by multiplying both sides of the equation by 3. This will eliminate the denominator:
[tex]\[ 3(d^2 + f) = a \][/tex]

4. Simplify the expression:
[tex]\[ a = 3d^2 + 3f \][/tex]

Thus, the solution for [tex]\( a \)[/tex] in terms of [tex]\( d \)[/tex] and [tex]\( f \)[/tex] is:
[tex]\[ a = 3d^2 + 3f \][/tex]