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

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.

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