Question

How do you solve `-7x + 5= 3+ 12+ 9x = 16x - 3x + 6- 2+ 12`?

Answer 1

As written there is no solution

Explanation:

Let's simplify all the expressions:

`-7x+5=3+12+9x=16x-3x+6-2+12`

`-7x+5=9x+15=13x+16`

I'm going to subtract by `-7x+5` to make the left hand term 0:

`-7x+5color(red)(-(-7x+5))=9x+15color(red)(-(-7x+5))=13x+16color(red)(-(-7x+5))`

`0=9x+7x-5+15=13x+7x-5+16`

`0=16x+10=20x+9`

Is there an `x` that will satisfy this?

`16x+10=0=>x=-10/16=-5/8`

`20x+9=0=>x=-9/20`

And so, as written, there is no solution to this system of equations.