Question

How is solving the equation a - ab = c for a different from the problems in this lesson? To solve it, you would use the ___ to write a - ab as a (1-b), and then ___ both sides by 1-b.

A. Factorization, divide
B. Addition, multiply
C. Subtraction, add
D. Exponentiation, subtract

Answer 1

The equation a - ab = c is solved by factorization, writing it as a(1-b), then dividing both sides by (1-b) to isolate a.

Step-by-step explanation:

To solve the equation a - ab = c for a, you would use factorization to write a - ab as a(1-b), and then divide both sides by (1-b). This is different from simply adding, subtracting, multiplying, or dividing both sides by a number because here you are factoring out a common term (a) which simplifies the expression and allows you to solve for a more easily.

The complete step-by-step solution would look something like this:

1. Start with the equation a - ab = c.
2. Factor out a from the left side to get a(1-b) = c.
3. Divide both sides by (1-b) to isolate a, assuming that b ≠ 1 (b is not equal to 1), to prevent division by zero.
4. After division, the solution for a is a = c / (1-b).

It is crucial to perform the same operation on both sides of the equation to maintain the balance, which is a fundamental principle of algebra.