Click here to load reader

Solving Nonlinear Inequalities - Cypress · PDF file Objective 5: Rational Inequalities Example: Solve the inequality 3 0 7 x x Graph the solution to the inequality. Write the solution

  • View
    10

  • Download
    0

Embed Size (px)

Text of Solving Nonlinear Inequalities - Cypress · PDF file Objective 5: Rational Inequalities...

  • Cypress College Math Department – CCMR Notes Solving Nonlinear Inequalities, Page 1 of 12

    Solving Nonlinear Inequalities

    Objective 1: Interval Notation and Set Builder Notation Inequality Graph Set Builder Notation Interval Notation

    Example: Graph the solution to the compound inequality. Write the solution in set builder notation and in interval

    notation. 3 1 5 11x or x or x     

  • Cypress College Math Department – CCMR Notes Solving Nonlinear Inequalities, Page 2 of 12

    Pause the video and try these problems.

    Graph the solution to the inequality. Write the solution to the inequality both in set builder notation and interval

    notation.

    1. 3 4x  

    2. 9x 

    3. 8 2x or x  

    Restart when you are ready to check your answers.

  • Cypress College Math Department – CCMR Notes Solving Nonlinear Inequalities, Page 3 of 12

    Objective 2: Use the Graph of a Function to Solve an Inequality

    Example: Solve the inequality 2 5 6x x 

    Write your answer in interval notation.

    ||| 106-3

    0

    0

    is negative

    is positive

  • Cypress College Math Department – CCMR Notes Solving Nonlinear Inequalities, Page 4 of 12

    Pause the video and try these problems.

    1. Consider the graph of the function 212y x x   .

    Use the graph to solve the inequality 212 0x x   .

    Write the solution to the inequality both in set builder

    notation and interval notation.

    Restart when you are ready to check your answer.

    Objective 3: Quadratic Inequalities

    Example: Solve the inequality 2 12 35x x  

    Write your answer in interval notation.

  • Cypress College Math Department – CCMR Notes Solving Nonlinear Inequalities, Page 5 of 12

    Example: Solve the inequality 220 3 2 0x x  

    Write your answer in interval notation.

    Example: Solve the inequality 2 5x 

    Write your answer in interval notation.

  • Cypress College Math Department – CCMR Notes Solving Nonlinear Inequalities, Page 6 of 12

    Pause the video and try these problems.

    Solve the inequality. Write your answer in interval notation.

    1. 2 6x x

    2. 26 5 0x x  

  • Cypress College Math Department – CCMR Notes Solving Nonlinear Inequalities, Page 7 of 12

    3. 2 7 0x  

    Restart when you are ready to check your answers.

    Objective 4: Polynomial Inequalities

    Example: Solve the inequality   4 2 0x x x   Write your answer in interval notation.

    Find critical values:

    1. Move all terms to one side.

    2. Factor.

    3. Set each factor equal to

    zero and solve.

  • Cypress College Math Department – CCMR Notes Solving Nonlinear Inequalities, Page 8 of 12

    Example: Solve the inequality 3 16x x

    Write your answer in interval notation.

    Example: Solve the inequality     3 2

    4 1 5 0x x x   

    Write your answer in interval notation.

  • Cypress College Math Department – CCMR Notes Solving Nonlinear Inequalities, Page 9 of 12

    Pause the video and try these problems.

    Solve the inequality. Write your answer in interval notation.

    1. 3 25 6x x x  

    2.     2

    3 8 0x x  

    Restart when you are ready to check your answers.

  • Cypress College Math Department – CCMR Notes Solving Nonlinear Inequalities, Page 10 of 12

    Objective 5: Rational Inequalities

    Example: Solve the inequality 3

    0 7

    x

    x

     

    Graph the solution to the inequality. Write the solution to the inequality both in set builder notation and interval

    notation.

    Example: Solve the inequality 3

    2 2x 

    Graph the solution to the inequality. Write the solution to the inequality both in set builder notation and interval

    notation.

    3 0 7 0

    3 7

    x or x

    x or x

       

      

    Find critical values:

    1. Move all terms to one side.

    2. Combine into one fraction.

    3. Factor numerator and denominator.

    4. Set each factor in both the numerator

    and denominator equal to zero and solve.

  • Cypress College Math Department – CCMR Notes Solving Nonlinear Inequalities, Page 11 of 12

    Example: Solve the inequality   

    2 7 3

    0 1

    x x

    x

      

    Graph the solution to the inequality. Write the solution to the inequality both in set builder notation and interval

    notation.

    Pause the video and try these problems.

    Solve the inequality. Write your answer in interval notation.

    1. 2 3

    0 1

    x

    x

     

  • Cypress College Math Department – CCMR Notes Solving Nonlinear Inequalities, Page 12 of 12

    2. 7

    7 3x 

    3.   

    2 2 1 4

    0 7

    x x

    x

       

    Restart when you are ready to check your answers.

Search related