solve for x

[muted ingot]

The answer key subtracted the right side and brought it to the left

What i did was multiply the denominator of the right side to the left

and then subtracted 5

and then made the denominators the same

and my answer is different than the answer key

Why does the method of multiplying the denominator not work?

Answer key:

[autumn maple]

Because if you multiply by (x-1)

The inequality sign > must be flipped when x-1 is negative

This is why we dont do that in inequalities

Because it's a pain in the ass

Remember that the inequality sign must be changed when we multiply it by a negative number

So you would to do 2 cases

Case x-1 is positive (inequality not flipped)
Case x-1 negative
(Inequality flipped)

It could work of course