I was told long ago way back when

Question

that when you have something like this

-x = 7

you solve for x by doing the following

(-x = 7)-

x = -7

but now that I think about it
your not actually multiplying by negative one what is actually happening is this right???

(- x = 7)-^-1

to get the negative ones to cancel out to give you this

x = -^-1 7

or simplified as x = - 7

so my question is does the negative in the denomenator matter??? can you always just move it up or take the opposite of the whole thing even with somehting like this

- x = (7x + 5x^2 - 3)^-1 (6x + 7x^2 -2)
do you sovle this the same way

(- x = (7x + 5x^2 - 3)^-1 (6x + 7x^2 -2))-^-1

x = (-(7x + 5x^2 - 3))^-1 (6x + 7x^2 -2)

is that correct???

Answer 1

my teachers use to tell me that you could just multiply by negative one because it dosen't change its value but that is not true as it changes its direction

Answer 2

Your teachers are right. I do not comprehend your thinking. You are obfuscating a very simple operation, multiplying each side by -1