Why arent there 4 cases to |$a+b$|=|$x+y$| With absolute value equations, such as $|x-4| = 3$ , to turn it into a normal equation we take the 2 cases of +- from the absolute value, which I understand.
What I dont however, is why for say $|x-3| = |2x+5|$, we only do $x+3 = \pm(2x+5)$. Shouldn't we have to do $\pm(x+3) = \pm (2x+5)$, as both sides expand out into a $\pm$ sign (because you would have the postive on the left matching to 2 cases on the right, and negative on the left matching to 2 on the right).
When I searched this up, it stated that there were only 2 cases, but that greatly confused me.

$$ 2x+5 =x-3$$ is the same equation as $$ -(2x+5)=-(x-3)$$
and $$(2x+5)=-(x-3) $$ is the same equation as $$-(2x+5)=x-3. $$
In each case, one is obtained from the other by multiplying both sides by $-1.$
