Question

The absolute value of 4x+5 =2x+4
/4x+5/=2x+4

Answer 1

if (we don't know yet) 4x+5 is positive, then the absolute value operation can be dropped (because it does not do anything to a positive number)
in other words, one possibility is
4x+5 = 2x+4
we can solve for x: add -2x to both sides
4x-2x + 5 = 2x - 2x + 4
2x+5 = 4
add -5 to both sides
2x = -1
x = -1/2

now check if it works:
4x+5= 4*(-1/2) + 5 = -2+5 = 3
and 2x+4 = 2*(-1/2) + 4 = -1+4 = 3
so it looks good.

the other possibility is 4x+5 is negative
if we multiply it by -1 we can drop the absolute value operator
-4x-5= 2x+4
now solve for x