Use the symbolic structure of the expression in the equation to explain why there is no solution to the equation

Question

7(4+2x)/ (28 +14x) =3

Answer 1

If you do a little factoring you can get this question. If we break up the equation into two parts we get part 1: 7(4+2x) and part 2: (28+14x). In part 1 you will notice that you can take a 2 out of the equation 4+2x, this is because it is a common factor. This leaves you with part 1 being 14(2+X). The reason why it is 14 is because you multiply the 2 that you took out with the 7 that is already there. 

 

For part 2 you also notice that there is a common factor of 14 that you can remove. This would leave you with 14(2+X) and you can't factor any further from here.

 

When recombining the two equations. You would get 14(2+X)/ 14(2+X). Since they are exactly the same they can be reduced down to 1. Therefore you would get 1 = 3 and clearly that is incorrect. Therefore there is no solution. 

Answer 2

Hi Tara, out there in Gibson Guitar land!

 

I think the issue is that when you multiply out the top of the fraction, it's going to be equal to the bottom part--any time the numerator and denominator are the same, the result is 1.

 

In other words, you'r dividing a number by itself, which is always 1. They gave you the answer of 3, which can not be the case.

 

"Symbolic structure" I'm assuming means you need to follow rules of the symbols, namely the distributive property...

 

("Symbolic structure" also had me thinking this was going to be a literature question!)

 

Hope this helps!

 

Matt