If we sold a car for cash, and turned around and purchaed a new car, is that cash for the sale considered income?

[MaryK1]

It is income, but it is only taxable income that has to be reported IF you received more than you paid for it (and any money you put into it like oil changes, new tires etc).  Cars rarely appreciate (except for some exotic and classic).  Your income from the sale of personal property is the price you received less your BASIS (what you paid plus) You cannot take a tax loss if you lost money on the sale of personal property.