2210.11 – Fraction Inequality

If ab<−cd\frac{a}{b}<-\frac{c}{d} where a,b,c,a, b, c, and dd are real numbers and bd≠0bd \neq 0, then:

  1. aa must be negative,
  2. aa must be positive,
  3. aa must be nonzero,
  4. aa must be negative or zero, but not positive,
  5. aa can be positive, negative, or zero.
Solution

The correct answer is e: aa can be positive, negative, or zero. Here are some examples:

aa is negative: −1151<−−12\frac{-1}{151}<-\frac{-1}{2}

aa is zero: 0151<−−12\frac{0}{151}<-\frac{-1}{2}

aa is positive: 1151<−−12\frac{1}{151}<-\frac{-1}{2}