Inverse functions and signs

Question

For finding an inverse of a simple function, algebraically I can solve for x:

$$ y = 2x+5 \tag{1}\label{1} $$

After moving quantity 2x to the left side, y to right and dividing by -2,

$$ x = {-y+5\over -2} \tag{2}\label{2}$$

The Symbolab app knows this isn't mathematically correct (it moved 5 to the left side, then dividing by 2) as it solves it as $$ x = {y-5\over 2}$$ Why is (2) wrong?

Answer 1

New edits (see revision history for old post):

$$\frac{-y+5}{-2}=\frac{-y+5}{-2}\times\frac{-1}{-1}=\frac{y-5}2$$

so you are just as correct.

Answer 2

After moving quantity $2x$ to the left side, $y$ to right and dividing by $-2$ $$y = 2x+5\Rightarrow -2x+y=5\Rightarrow -2x=5-y\Rightarrow x=\frac{5-y}{-2}=\frac{y-5}{2}$$

Answer 3

$x = \frac{- y + 5}{-2}$

Taking -1 common from numerator,

$x = \frac{-1(y - 5)}{-2}$

$x = \frac{y - 5}{2}$

Both expressions are same.

I think most of the time we try that our starting variable terms should be positive. And in above equation its possible. So maybe your app also work in that way.