Question 8

b = c/a - c

To solve the equation ab - c = cb for b, we can rearrange it to isolate b, leading us to the conclusion that b equals c/a - c when a is not equal to c.

A) a/c - a

This option does not correctly solve for b based on the original equation. Substituting a in place of b does not satisfy the equation ab - c = cb, especially since it suggests a direct relationship between a and b that is not supported by the given problem.

B) c/a - c

This is the correct answer as it effectively rearranges the equation to isolate b. By manipulating the equation ab - c = cb, we can derive b = c/a - c, which satisfies the condition that a is not equal to c.

C) 2c/a

This option is not accurate because it suggests that b is simply double the fraction of c over a, which does not align with the original equation. Substituting this value for b would not yield a consistent result when plugged back into the equation.

D) 2c/a

This option is identical to C and also does not provide a valid solution for b. It fails to maintain the relationship described in the original equation and does not account for the necessary variable manipulation.

Conclusion

The solution b = c/a - c is derived directly from rearranging the original equation ab - c = cb, maintaining the condition that a is not equal to c. All other options fail to correctly isolate b or do not reflect the necessary algebraic manipulation, making option B the only valid answer.