The price of gasoline seems to remain the same [1].
[1] https://www.eia.gov/todayinenergy/images/2017.05.26/chart2.p...
If prices for goods are low so are the wages of the workers that produce them. If there was a way for workers to get some of the central bank money they would spend it on consumer goods which drive up demand for consumer goods and those consumer goods have to be produced by workers which drives the incomes of those workers up.
So when I am talking about consumer inflation I am not just talking about the prices of services and goods but also the incomes of workers. These things are linked extremely tightly. High incomes drive up consumer inflation and consumer inflation drives up incomes. If you can get rich without involving workers you have found a recipe for growing wealth inequality precisely because you avoided consumer inflation.
So by definition low consumer inflation is associated with inequality. If there was consumer inflation but no asset inflation the relative wealth of asset owners would diminish and the relative wealth of people with income would increase.
High consumer inflation is generally associated with low unemployment because the scarcity of workers is driving up prices of consumer goods. Imagine a medieval country that is going into debt to start a war. They are buying up all the food for the soldiers and thereby drive up the prices. If everyone is already at full employment because e.g. they are doing subsistence farming and barely grow enough food for themselves + some taxes then what happens is that food becomes unaffordable for farmers and you are taking away all the food from the farmers and giving it to the soldiers. This obviously results in a famine because those farmers need that food to feed themselves and grow more food next year.
However, we are not a medieval country that has hit its maximum economic output. There is slack in the system. We have unemployment, especially youth unemployment in European countries. If you increase demand for workers you decrease unemployment despite introducing more money into the system. If you figure out how to print money and somehow do not create more demand for workers you end up keeping employment low. As long as unemployment is high you can keep printing more money endlessly. That's not an argument in favor of printing more money, it means that you should spend your money on the right things instead.