- #1

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This is a set of linear equations that I am asked to solve. That being said I am getting hung up on how to distribute a fraction. The answer is x=9, however, I am getting x=36 and the step I do not understand is distributing the fraction.

We then get setup with 2*((31-5y)/14)-3y = -29 by solving for x.

We then distribute the 2 this gives us ((62-10y)/14)-3y = -29.

This can also be written as 1/14 *(62-10y)-3y = -29.

Now why can't we distribute this is the inverse? e.g. 1/14*14/1 = 1

(62-10y)-3y = -29*14 -> (62-10y)-3y = -406

That gets us 62-13y = -406 then do some basic arithmetic ->

-62, -62

-13y = -465, divide by -13 -> y = 36

How is this method incorrect? I'm very frustrated because I have spent hours on this. I can see another method of performing this would be multiply by the inverse ->

(62-10y)/14)-3y = -29

Multiple by the inverse ((62-10y)/14) * ((14)/(62-10y)) ->

62-10y-3y = -29* ((14)/(62-10y)) and then I go nowhere.

I will be incredibly happy if someone can help me to understand this. Thanks kindly.