It costs dollars to ship a package that weighs pounds if and only if . If Alan’s package weighs pounds and costs dollars to ship, which of the following must be true?
The wording of this question is horrible. It tells you about Allan who shipped a package and it cost him d Dollars to ship.
It wastes your time to try and understand what d has to do with the question (hint: NOTHING).
You have a package that weighs anything between 6 and 10 pounds. Shipping packages that weigh in between 6 and 10 pounds cost the same (d) regardless of the actual weight of the package.
That means Allan’s package must weigh something between 6 and 10 pounds.
You are asked to find the expression that best describe the relation between the data above and the weight (p) of this specific package.
All the answers have absolute value in them – that is they strip the expression inside of them of it’s sign (be it positive or negative) and place a positive sign instead.
Now Allan’s package can weigh 6, 7.5, 7.8, 9.9 or 10 pounds – all are OK.
The answer, in this question, must always be true (think why). You can plug in 6, 8, and 10. This will nullify A, B, D, and E.
Another way to think about it is that with absolute value expression we are measuring the distance (positive) from a mid point. In our case the difference between 10 and 6 is 4 and the mid-point is 8. If we measure the difference between the actual weight of Allan’s package and 8 – it’s absolute value must always be smaller or equal to 2.