TBIL-Precal Equations, Inequalities, and Applications (EQ)

Chapter 1 Equations, Inequalities, and Applications (EQ)

Objectives

How do we find solutions of equations?

By the end of this chapter, you should be able to...

Solve linear equations in one variable. Solve linear inequalities in one variable and express the solution graphically and using interval notation.
Solve application problems involving linear equations.
Given two points, determine the distance between them and the midpoint of the line segment connecting them.
Solve linear equations involving an absolute value. Solve linear inequalities involving absolute values and express the answers graphically and using interval notation.
Solve quadratic equations using factoring, the square root property, completing the square, and the quadratic formula and express these answers in exact form.
Solve rational equations.
Solve quadratic inequalities and express the solution graphically and with interval notation. Solve rational inequalities and express the solution graphically and using interval notation.

Readiness Assurance.

Before beginning this chapter, you should be able to...

Plot points on the coordinate plane.
- Review and Practice: Khan Academy
  ¹
  www.khanacademy.org/math/cc-sixth-grade-math/x0267d782:coordinate-plane/cc-6th-coordinate-plane/v/the-coordinate-plane
Determine whether a given value is a solution to an equation.
- Review: YouTube (Megan MathTeacher Snow)
  ²
  www.youtube.com/watch?v=rE47-V-FX0M
- Review and Practice: Khan Academy
  ³
  www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-equations-and-inequalities/cc-6th-intro-equations/v/testing-solutions-to-equation
Solve two step linear equations.
- Review: YouTube (Mathispower4u)
  ⁴
  www.youtube.com/watch?v=9ITsXICV2u0
- Review and Practice: Khan Academy
  ⁵
  www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-variables-expressions/cc-7th-2-step-equations-intro/v/solving-equations-1
Use interval notation.
- Review: YouTube (The Organic Chemistry Tutor)
  ⁶
  www.youtube.com/watch?v=Ww7xtG2S7IM
- Practice: IXL
  ⁷
  www.ixl.com/math/algebra-1/interval-notation
Find the absolute value of real numbers.
- Review and Practice: Khan Academy
  ⁸
  www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-negative-number-topic/cc-6th-absolute-value/v/absolute-value-of-integers
Use the Pythagorean Theorem to find side lengths of right triangles.
- Review and Practice: Khan Academy
  ⁹
  www.khanacademy.org/math/algebra-basics/alg-basics-equations-and-geometry/alg-basics-pythagorean-theorem/v/the-pythagorean-theorem
Factor quadratic equations.
- Review and Practice: Khan Academy
  ¹⁰
  www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratics-multiplying-factoring/x2f8bb11595b61c86:factor-quadratics-strategy/a/factoring-quadratics-in-any-form
Solve one-step problems involving distance, rate, and time.
- Review: YouTube (Krista King Math)
  ¹¹
  www.youtube.com/watch?v=Zl6zUBCgLbU
- Review: YouTube (Mathispower4u)
  ¹²
  www.youtube.com/watch?v=lMO1L_CvH4Y
Use the percent equation.
- Review and Practice: Khan Academy
  ¹³
  www.khanacademy.org/math/cc-sixth-grade-math/x0267d782:cc-6th-rates-and-percentages/cc-6th-percent-problems/v/finding-percentages-example
Simplify square roots of positive numbers.
- Review and Practice: Khan Academy
  ¹⁴
  www.khanacademy.org/math/algebra/x2f8bb11595b61c86:rational-exponents-radicals/x2f8bb11595b61c86:simplifying-square-roots/v/simplifying-square-roots-1
Simplify square roots of negative numbers using \(i\text{.}\)
- Review and Practice: Khan Academy
  ¹⁵
  www.khanacademy.org/math/algebra-home/alg-complex-numbers/alg-the-imaginary-numbers/v/imaginary-roots-of-negative-numbers

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