In math students think that the function just removes negative signs, and actually that is basically what happens...
BUT !!! the definition that you want is that absolute value is a measure of how far (distance) you are from ZERO.... and note that distances are not negative...
If you run out of gas one mile in front of behind a gas station, you have to travel "one mile" you don't walk "negative one mile"...
forward one mile or backward one mile are both "one mile" just in different directions
because the cost stays the same and you would multiply blank gallons of gas by 1.50 every time so it is proportional. For example: it would be $1.50 to 1 gallon, $3 to 2 gallons, $4.50 to 3 gallons and would keep going like that, adding the same amount every time