Question

Find all values of a such that there is no value of b that satisfies the equation (2-b)/(3-b) = 5a

Answer 1

You could first experiment with various values of "a." What if "a"=0? Could you find "b" in that case?

Or y ou could experiment with various values of "b". What if "b" = 3? Could you find "a?"

Next, determine the value or values of "a" at which (2-b)/(3-b) = 0.
Likewise, determine the value or values of "b" at which (2-b)/(3-b) = 0 or is not defined.

Although this approach is more experimental than algebraic, it should eventually help you come up with "values of a for which no value of b satisfies the equation."

Answer 2

3 is one answer I know that, There are answers to this question. my AoPS book says it itself.

Answer 3

b cannot be 3. Can you explain why?
Do you need further help?

Answer 4

Correct it cannot be 3. But there is an answer to this. I need step by sgep into this problem because I am new to Intermediate Alg, would appreciate ur help

Answer 5

And btw b can't be three because it would be undefined.

Answer 6

@mathmale

Answer 7

True, b)/(3-b) is undefined if b = 3. Does this place any restrictions on the value of a?

Have you tried any of my other (earlier) suggestions?

Answer 8

well it doesnt because A stands by itself.

Answer 9

@mathmale

Answer 10

perhaps a good way to look at this is to translate it as "find the range of\(\frac{2-b}{3-b}\)

Answer 11

that answer might be completely obvious
if not, let me know

Answer 12

or even
"find the range of \[f(x)=\frac{x-2}{x-3}\]"

Answer 13

Good point. Review the mathematical meaning of "range," please. Then identify the range of the function 5a = (2-b)/(3-b).