If `(5)/(6)lt(1)/(2)x-(1)/(2)ylt(3)/(2)`, then what is one possible of `x-y`?

Answer

C

Explanation

Difficult:Easy:
Category: Heart of Algebra/ Inequalities
Strategic Advice: When there is only one equation (or inequlality), but two variables, you can't solve for either variable. Instead, try to manipulate what is given to make it look like what you want (usually through mutliplication or division).
Getting to the Answer. Compare the variable terms between the two inequality symbols to the exression you're looking for: `(1)/(2)x-(1)/(2)y` is exactly half of `x-y`, so multiply the entire inequality by 2. The inequality becomes `(5)/(3)ltx-ylt3`. Grid in any value between `1(2)/(3)` and 3 (but not `1(2)/(3) or 3`), such as 2 or 2.5.