In the equation b/4 = (q² /8) (A+L), how do you solve for A?

To solve for A in the equation b/4 = (q² /8) (A + L), we start by isolating the term containing A. The process involves a few algebraic manipulation steps.

First, we can multiply both sides of the equation by 8 to eliminate the fraction on the right side. This gives us:

8 * (b/4) = q² * (A + L)

This simplifies to:

2b = q² * (A + L)

Next, we divide both sides by q² to isolate the term (A + L):

(2b/q²) = A + L

Now, we need to isolate A by subtracting L from both sides:

A = (2b/q²) - L

This derivation shows that the correct formulation for A is indeed (2b/q²) - L, aligning with the provided answer choice.

This careful algebraic rearrangement highlights how we manipulate equations to isolate variables, which is a fundamental skill in both engineering calculations and applying physical principles effectively.