Question

Solve for c in the equation a(b-c) = d. A) c = ab - d/b B) c = ab - d/a C) c = ab + d/a D) c = d - ab/a

Answer 1

Option B is correct because, after expanding and rearranging the equation
`\(a(b-c) = d\),` isolating
`\(c\) yields \(c = ab - d/a\),` as shown through algebraic manipulation.

Step-by-step explanation:

To solve for c in the equation
`\( a(b-c) = d \)`, we can start by expanding the left side of the equation. Applying the distributive property, we get ab - ac = d . Next, we isolate c by moving ac to the other side of the equation, resulting in ab = d + ac . To solve for c , we can then subtract d from both sides and divide by a , yielding the solution
`c = (ab - d)/a .`Therefore, the correct option is B) c = ab - d/a .

In detail, we begin with the equation ab - ac = d . Rearranging terms, we have ab = d + ac . To isolate c , we subtract d from both sides, resulting in ab - d = ac . Finally, by dividing both sides by a , we obtain the solution c = (ab - d)/a . This matches the form of the correct answer B) c = ab - d/a . The process involves algebraic manipulation and follows logical steps to arrive at the final solution.

In summary, the solution to the equation a(b-c) = d is c = ab - d/a . The method involves expanding, rearranging, and isolating the variable \( c \) through a series of algebraic operations.