2210.11 – Fraction Inequality

Tags:Problem Set 1Algebra/TrigonometryPre-Calculus

If ab<cd\frac{a}{b}<-\frac{c}{d} where a,b,c,a, b, c, and dd are real numbers and bd0bd \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.


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}