Question

How can you create inequalities in one variable and use them to solve problems?

Answer 1

Usually, you create the inequality by casting the problem statement into mathematical terms. Then, solving the inequality can answer the question posed by the problem statement.

Example:
   I want to carpet my 1600 ft² house, but I can only afford to spend $3000. Tax and installation costs are expected to add 20% to the total cost of the carpet. What price range of carpet should I be looking at in term of dollars per square yard?

Solution:
  Let p represent the price per square yard of carpet. The problem statement tells me
   (1600 ft²)×((1 yd)/(3 ft))²×p×(1 + 0.20) ≤ $3000 . . . . . created inequality
   p×((1600×1.20)/9 yd²) ≤ $3000 . . . . . . . . . . . . . . . . . simplify left side
   p ≤ $14.06/yd²
I can afford carpet that costs less than $14.06 per square yard.