Final answer:
Solving (fb + 3b = d) for (b) involves factoring out (b) to get (b(f + 3) = d) and isolating (b) as (b = d (f + 3)), expressing (b) in terms of (d) and (f).
Step-by-step explanation:
In solving the equation (fb + 3b = d) for (b), the initial step involves grouping like terms on the left side. Recognizing that both terms contain (b), factoring (b) out yields (b(f + 3) = d). To isolate (b), divide both sides by the quantity (f + 3), resulting in (b = d (f + 3)). This solution expresses (b) in terms of (d) and (f), signifying that (b) is determined by the ratio of (d) to the sum of (f) and 3. Essentially, the equation unveils a relationship where (b) can be derived from specific values of (d) and (f), offering a clear representation of how changes in (d) and (f) affect the value of (b).