PRECAL.MATH.5.L

Solve rational inequalities with real coefficients by applying a variety of techniques and write the solution set of the rational inequality in interval notation in mathematical and real-world problems.

Precalculus · Texas Essential Knowledge and Skills (TEKS) · TEKS 2012

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Vocabulary
polynomial inequalitiesreal coefficientstechniquessolution setinterval notationmathematical problemsreal-world problems
Skills
  • solve (polynomial inequalities with real coefficients) #dok2
  • apply (variety of techniques for solving polynomial inequalities) #dok2
  • write (solution set in interval notation) #dok1
  • analyze (context of mathematical and real-world problems involving polynomial inequalities) #dok3
Learning Targets
  • I can identify and restate a polynomial inequality with real coefficients. #dok1
  • I can write the solution set of a polynomial inequality in interval notation. #dok1
  • I can solve polynomial inequalities using factoring or sign charts. #dok2
  • I can apply appropriate techniques to solve polynomial inequalities with real coefficients. #dok2
  • I can analyze a real-world scenario represented by a polynomial inequality and interpret the results. #dok3
  • I can justify and communicate the solution process for a polynomial inequality in mathematical notation and context. #dok3
Big Ideas
  • Polynomials and their inequalities can represent and solve a variety of mathematical and real-world problems, making them powerful modeling tools.
  • Expressing solution sets in interval notation is essential for clearly and accurately communicating the results of polynomial inequalities.
Essential Questions
  • How does solving a polynomial inequality differ from solving a polynomial equation?
  • Why is interval notation an effective way to express solution sets for inequalities?
  • What techniques can be used to solve polynomial inequalities with real coefficients?
  • How can polynomial inequalities be applied to solve problems in real-world contexts?
  • How do the solutions of polynomial inequalities inform decision-making in mathematical modeling?