This document discusses linear inequalities and their applications. It defines linear inequalities and introduces using them to represent real world scenarios involving constraints. An example is provided where a nursery sold maple and birch trees for different prices, with the total being over $1500. Linear inequalities are written and graphed to represent the possible combinations of trees sold based on this information. The graph is then used to determine if specific quantities of each type of tree could have been sold.

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Ex. On Earth Day, a nursery sold more than $1500 worth of maple
and birch trees. The maple trees were sold for $75 and the birch
trees were sold for $50.
a) Write a linear inequality to represent the possible combinations of
trees sold. Are there any restrictions?
b) Graph the inequality.
c) Use the graph to determine:
i) Could the nursery have sold 13 of each type of tree?
ii) If 14 of one type and 9 of the other type could have been sold.
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