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Equations & inequalities furqan m lodhi

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  • 1. Furqan munir lodhi bc141004 maju
  • 2. Equations & Inequalities
  • 3. Equation Equation are the basic mathematical tool for solving real-world problem To solve the problem, we must know how to construct equation that model real-life situations.
  • 4. equation Linear Equation Quadratic Equation Polynomial equation
  • 5. equation Linear Equation Simultaneous Equation for 2 x 2 system Quadratic Equation Addition and subtraction Factorization Completing the square Formulae Substitution Elimination
  • 6. Linear equations Addition and subtraction Multiplication and division
  • 7. Factorization Formulae Completing the square If a = 1
  • 8. Solving of quadratic equation • By factoring 1. Solve the equation Solution: By completing the square 2. Solve the equation Solution:
  • 9. Simultaneous equation • Simultaneous equation has two or more equation that has similar set of solution. Linear equation can be solved by using substitution and elimination method.
  • 10. SimultaneousEquationfor 2 x 2 system Substitution Elimination
  • 11. example
  • 12. inequalities • An inequality says that two values are not equal. a ≠ b says that a is not equal to b There are other special symbols that show in what way things are not equal. a < b says that a is less than b a > b says that a is greater than b (those two are known as strict inequality) a ≤ b means that a is less than or equal to b a ≥ b means that a is greater than or equal to b.
  • 13. inequality Inequalities Absolute value Linear Inequality Quadratic Inequality
  • 14. Inequalities Linear Inequality Quadratic Inequality Single Inequality Double Inequality
  • 15. Absolutevalue , 0 , 0 x if x x x if x      • Properties of absolute value abbaiii aaii ai    )( )( 0)( • Absolute value equations or x = -a with a is real number positive axax 
  • 16. Example :
  • 17. Inequality • Linear inequality with one variable
  • 18. THE END Please Do a Lot of Exercises JUST REMEMBER: