If ab - c = cb, and a neq c, then b =

Rationale

b = c/a - c.

To solve for b in the equation ab - c = cb, we can rearrange and isolate b, leading to the correct expression b = c/a - c. This manipulation shows the direct relationship between b and the variables a and c.

A (a/c-a) YOUR ANSWER

This choice incorrectly suggests that b can be expressed in terms of a and c in a way that does not satisfy the original equation. The term a/c introduces a division that is irrelevant to the isolation of b in our derived equation.

B (c/a-c) CORRECT

This is the correct choice as it accurately represents b after rearranging the given equation ab - c = cb. By isolating b, we find that b equals c divided by a minus c, which is consistent with the manipulation of the original equation.

C (0) YOUR ANSWER

This choice implies that b is zero, which would only hold true under specific conditions not stipulated in the problem. Since a and c are not equal and no other conditions suggest that b equals zero, this choice is incorrect.

D (2c/a) YOUR ANSWER

This option posits that b is twice c divided by a, which does not arise from the original equation. The factor of 2 is extraneous and does not correspond to any manipulation of the equation ab - c = cb.

Conclusion

The equation ab - c = cb can be rearranged to yield the expression for b as c/a - c, making choice B the accurate answer. Other options fail to satisfy the algebraic rearrangement necessary to isolate b or introduce incorrect assumptions about its value. Understanding this relationship is essential for solving similar algebraic equations effectively.

If ab - c = cb, and a neq c, then b =

b = c/a - c.

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