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

We already know that he is trying to save 10 dollars a week and his goal is 300 so we know that has to be in the equation. 160 is the only one not mentioned in the back round information so we can say that the 160 dollars is the amount of money he already had saved before he started working