Iknow the solution is "no solution" but can someone show me the steps? (absolute value equation) |4x+7|=2x+3

If x>-7/4 then inside Absolute Value is positive 4x+7=2x+3 --->2x=-4 --->x=-2 but we said if x>-7/4 so x=-2 is not acceptable
if x<-7/4 then inside Absolute Value is negative -4x-7=2x+3 --->6x=-10--->x=-10/6=-5/3 but we said x<-7/4 so x=-5/3 is not acceptable