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Algebra equations & inequalities

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Presentación para una introducción a las inequaciones.

Presentación para una introducción a las inequaciones.

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Algebra equations & inequalities Algebra equations & inequalities Presentation Transcript

  • Algebra: Equations & Inequalities
    Miguel Pérez Fontenla
    November, 2010
  • Algebra: Equations & Inequalities
    Whatisanequation?
    Anequationis a mathematicalstatement
    Example:
  • Algebra: Equations & Inequalities
    Properpies of equations
    Property 1 - Adding or Subtracting a Number
    An equation is not changed when the same number is added or subtracted from both sides of the equality.
    Example: A = B (adding 4 to both sides gives)⇔ A + 4 = B + 4
    Property 2 - Multiplying or dividing by a Number
    An equation is not changed if both sides are multiplied or divided by the same number.
    Example: A = B (Multiplying both sides by 2 gives) ⇔ 2A = 2B
    A = B (Dividing both sides by 3 gives) ⇔ A/3 = B/3
     
  • Algebra: Equations & Inequalities
    Types of equations?
    • Linear equations
    • Quadraticequations
    • Biquadratic
    • Simultaneousequations
    • Linear
    • Quadratic
    • Rationalequations
    • Irrationalequations
    • Othertypes
  • Algebra: Equations & Inequalities
    Solving linear equations
    No parenthesis
    No fractions
    Isolate x tosideone
    Obtain x
    Checkyourwork
  • Algebra: Equations & Inequalities
    Solvingquadraticequations
    No parenthesis
    No fractions
    Isolateeverything
    tosideone
    Obtain x
    Checkyourwork
  • Algebra: Equations & Inequalities
    Whatisaninequality?
  • Algebra: Equations & Inequalities
    Whatisaninequality?
    Example:
  • Algebra: Equations & Inequalities
    Properpies of inequalities
    Property 1 - Adding or Subtracting a Number
    The sense of an inequality is not changed when the same number is added or subtracted from both sides of the inequality.
    Example: 9 > 6 (adding 4 to both sides gives) ⇔ 9 + 4 > 6 + 4
    Property 2 - Multiplying by a Positive Number
    The sense of the inequality is not changed if both sides are multiplied or divided by the same positive number.
    Example: 8 < 15 (Multiplying both sides by 2 gives) ⇔ 8 × 2 < 15 × 2
    Property 3 - Multiplying by a Negative Number
    The sense of the inequality is reversed if both sides are multiplied or divided by the same negative number.
    Example: 4 > −2 (Multiplying both sides by -3 gives) ⇔ 4 × −3 < −2 × −3 ⇔ −12 < 6 (Note the change in the sign used)
     
  • Algebra: Equations & Inequalities
    Solving Linear inequalities
    No parenthesis
    No fractions
    Isolate x tosideone
    Obtain x
    Check
  • Algebra: Equations & Inequalities
    Linear inequalities: GraphicSolution
  • Algebra: Equations & Inequalities
    Solvingquadraticinequalities
    No parenthesis
    No fractions
    Isolateeverything
    tosideone
    Obtainsolutions of theequation
    Set theintervalssolution
    Check
  • Algebra: Equations & Inequalities
    Quadraticinequalities: GraphicSolution
  • Algebra: Equations & Inequalities
    Putinginto a Graph
    A linear equationwithtwo variables can berepresentedby a straight line in theplane.
    A quadraticequationwithtwo variables can berepresentedby a parabole in theplane.
  • Algebra: Equations & Inequalities
    Solvingsimultaneous linear inequalities
  • Algebra: Equations & Inequalities
    Solvingsimultaneousinequalities
  • Algebra: Equations & Inequalities
    Solvingsimultaneousquadraticinequalities
  • Algebra: Equations & Inequalities
    Solvingsimultaneousinequalities
  • Algebra: Equations & Inequalities
  • Algebra: Equations & Inequalities
  • Algebra: Equations & Inequalities