If (x-1)/3 = k and k=3, what is the value of x?

Varna Venugopal

Thanks for the easy way!!!! :)
I really knew the answer for this question but I liked the way you explained!!

Jul 30, 2017 •Reply

Cydney Seigerman, Magoosh Tutor

On Chris's behalf, you're very welcome :D

Jul 30, 2017 •Reply

Clarissa Perez

I'm confused ! Why didn't you multiply the 3 by x and -1 ? but you chose to multiply it to the denominator (3) ?

Dec 28, 2017 •Reply

David Recine, Magoosh Tutor

In the solution, you actually DO multiply 3 by the numerator (x-1) and not the denominator (3). In fact, when multiplying a fraction, you always multiply by numerator and not denominator. to give a simple example of why, (1/2)*2 = 2/2, or 1. (1/2)*2 does NOT equal 2/4 (2 multiplied by both numerator and denominator), nor does it equal 1/4 (2 multiplied by denominator only).

So with (x-1)/3 why does multiplying 3 by numerator unchanged, while the denominator IS affected and goes away? It's because if you multiply the numerator by a number that is the same as the number IN the denominator, the number you multiplied on top and the number of the denominator on the bottom cancel each other out. So, in [3(x-1)]/3, the 3 on top that is multiplied by x-1 cancels out the 3 on the bottom. then, with no more three on the top OR the bottom, all you have left is x+1.

It's important to remember that "cancelling out" doesn't mean the denominator has truly gone away. What's really happened is that the 3 on top and 3 on the bottom make the fraction 3/3, which is multiplied by the denominator for your answer.

In other words, [3(x-1)]/3 is the same as (3/3)(x-1). And 3/3 itself is the same as 1. So, [3(x-1)]/3 = (1)(x-1), which is the same as just (x-1), since any value multiplied by just 1 stays exactly the same.

On the other hand, let's say you multiplied (x-1)/3 by a number that is bigger than 3, but divisible by it? for example, say you had [6(x-1)]/3. This is the same as (6/3)*(x-1). 6/3 = 2, so what we really have in this case is (2)(x-1), or 2x-2 when simplified. Here, since the cancelling out doesn't simply create the number 1, (x-1) isn't isolated alone. And the denominator doesn't "go away," but instead goes into the 6 in the numerator to make a 2.

Does this make sense? Let me know if you have any questions.

Jan 15, 2018 •Reply