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Consider the inequality 0.5x - 2 < 5/(2x). Rewrite the inequality so that there is a single, simplified expression on one side and a zero on the other side. List all the factors of the rational expression in a table, and determine on which intervals the inequality is true. An economist for a sporting goods company estimates the revenue and cost functions for the production of a new snowboard. These functions are R(x) = -x^2 + 10x and C(x) = 4x + 5, where x is the number of snowboards produced, in thousands. The average profit is defined by the function AP(x) = P(x) / x, where P(x) is the profit function. Determine the production levels that make AP(x) > 0.

Explore how to solve a rational inequality and analyze production levels for average profit in snowboard manufacturing. Learn to simplify inequalities, find intervals, and apply revenue-cost-profit formulas, suitable for Grades 10-12.

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