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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