Solving Equations (Algebra 2)

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Students review properties of equality, used for solving equations.

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Solving Equations (Algebra 2)

  1. 1. Solving Equations
  2. 2. You'll Learn To: Solving Equations Vocabulary 1) open sentence 2) equation 3) solution <ul><li>Translate verbal expressions into algebraic expression and equations and vice versa. </li></ul><ul><li>Solve equations using the properties of equality. </li></ul>
  3. 3. A mathematical sentence (expression) containing one or more variables is called an open sentence . Solving Equations
  4. 4. A mathematical sentence (expression) containing one or more variables is called an open sentence . A mathematical sentence stating that two mathematical expressions are equal is called an _________. Solving Equations
  5. 5. A mathematical sentence (expression) containing one or more variables is called an open sentence . A mathematical sentence stating that two mathematical expressions are equal is called an _________. equation Solving Equations
  6. 6. A mathematical sentence (expression) containing one or more variables is called an open sentence . A mathematical sentence stating that two mathematical expressions are equal is called an _________. equation Open sentences are neither true nor false until the variables have been replaced by numbers. Solving Equations
  7. 7. A mathematical sentence (expression) containing one or more variables is called an open sentence . A mathematical sentence stating that two mathematical expressions are equal is called an _________. equation Open sentences are neither true nor false until the variables have been replaced by numbers. Each replacement that results in a true statement is called a ________ of the open sentence. Solving Equations
  8. 8. Solving Equations A mathematical sentence (expression) containing one or more variables is called an open sentence . A mathematical sentence stating that two mathematical expressions are equal is called an _________. equation Open sentences are neither true nor false until the variables have been replaced by numbers. Each replacement that results in a true statement is called a ________ of the open sentence. solution
  9. 9. To solve equations, we can use properties of equality. Some of these equivalence relations are listed in the following table. Solving Equations
  10. 10. To solve equations, we can use properties of equality. Some of these equivalence relations are listed in the following table. Reflexive Symmetric Transitive Substitution Solving Equations Properties of Equality Property Symbol Example
  11. 11. To solve equations, we can use properties of equality. Some of these equivalence relations are listed in the following table. Reflexive Symmetric Transitive Substitution For any real number a , a = a , Solving Equations Properties of Equality Property Symbol Example
  12. 12. To solve equations, we can use properties of equality. Some of these equivalence relations are listed in the following table. Reflexive Symmetric Transitive Substitution For any real number a , a = a , – 5 + y = – 5 + y Solving Equations Properties of Equality Property Symbol Example
  13. 13. To solve equations, we can use properties of equality. Some of these equivalence relations are listed in the following table. Reflexive Symmetric Transitive Substitution For any real number a , a = a , For all real numbers a and b , If a = b, then b = a – 5 + y = – 5 + y Solving Equations Properties of Equality Property Symbol Example
  14. 14. To solve equations, we can use properties of equality. Some of these equivalence relations are listed in the following table. Reflexive Symmetric Transitive Substitution For any real number a , a = a , For all real numbers a and b , If a = b, then b = a – 5 + y = – 5 + y If 3 = 5x – 6, then 5x – 6 = 3 Solving Equations Properties of Equality Property Symbol Example
  15. 15. To solve equations, we can use properties of equality. Some of these equivalence relations are listed in the following table. Reflexive Symmetric Transitive Substitution For any real number a , a = a , For all real numbers a and b , If a = b, then For all real numbers a , b , and c . If a = b, and b = c, then b = a a = c – 5 + y = – 5 + y If 3 = 5x – 6, then 5x – 6 = 3 Solving Equations Properties of Equality Property Symbol Example
  16. 16. To solve equations, we can use properties of equality. Some of these equivalence relations are listed in the following table. Reflexive Symmetric Transitive Substitution For any real number a , a = a , For all real numbers a and b , If a = b, then For all real numbers a , b , and c . If a = b, and b = c, then b = a a = c – 5 + y = – 5 + y If 3 = 5x – 6, then 5x – 6 = 3 If 2x + 1 = 7 and 7 = 5x – 8 then, 2x + 1 = 5x – 8 Solving Equations Properties of Equality Property Symbol Example
  17. 17. To solve equations, we can use properties of equality. Some of these equivalence relations are listed in the following table. Reflexive Symmetric Transitive Substitution For any real number a , a = a , For all real numbers a and b , If a = b, then For all real numbers a , b , and c . If a = b, and b = c, then If a = b, then a may be replaced by b and b may be replaced by a. b = a a = c – 5 + y = – 5 + y If 3 = 5x – 6, then 5x – 6 = 3 If 2x + 1 = 7 and 7 = 5x – 8 then, 2x + 1 = 5x – 8 Solving Equations Properties of Equality Property Symbol Example
  18. 18. To solve equations, we can use properties of equality. Some of these equivalence relations are listed in the following table. Reflexive Symmetric Transitive Substitution For any real number a , a = a , For all real numbers a and b , If a = b, then For all real numbers a , b , and c . If a = b, and b = c, then If a = b, then a may be replaced by b and b may be replaced by a. b = a a = c – 5 + y = – 5 + y If 3 = 5x – 6, then 5x – 6 = 3 If 2x + 1 = 7 and 7 = 5x – 8 then, 2x + 1 = 5x – 8 If (4 + 5) m = 18 then 9m = 18 Solving Equations Properties of Equality Property Symbol Example
  19. 19. Sometimes an equation can be solved by adding the same number to each side or by subtracting the same number from each side or by multiplying or dividing each side by the same number. Solving Equations
  20. 20. Sometimes an equation can be solved by adding the same number to each side or by subtracting the same number from each side or by multiplying or dividing each side by the same number. Addition and Subtraction Properties of Equality For any real numbers a , b , and c , if a = b, then Solving Equations
  21. 21. Sometimes an equation can be solved by adding the same number to each side or by subtracting the same number from each side or by multiplying or dividing each side by the same number. Addition and Subtraction Properties of Equality For any real numbers a , b , and c , if a = b, then a = b + c + c Solving Equations
  22. 22. Sometimes an equation can be solved by adding the same number to each side or by subtracting the same number from each side or by multiplying or dividing each side by the same number. Addition and Subtraction Properties of Equality For any real numbers a , b , and c , if a = b, then a = b + c + c a = b - c - c Solving Equations
  23. 23. Sometimes an equation can be solved by adding the same number to each side or by subtracting the same number from each side or by multiplying or dividing each side by the same number. Addition and Subtraction Properties of Equality For any real numbers a , b , and c , if a = b, then a = b + c + c a = b - c - c Example: If x – 4 = 5, then Solving Equations
  24. 24. Sometimes an equation can be solved by adding the same number to each side or by subtracting the same number from each side or by multiplying or dividing each side by the same number. Addition and Subtraction Properties of Equality For any real numbers a , b , and c , if a = b, then a = b + c + c a = b - c - c Example: If x – 4 = 5, then x – 4 = 5 + 4 + 4 Solving Equations
  25. 25. Sometimes an equation can be solved by adding the same number to each side or by subtracting the same number from each side or by multiplying or dividing each side by the same number. Addition and Subtraction Properties of Equality For any real numbers a , b , and c , if a = b, then a = b + c + c a = b - c - c Example: If x – 4 = 5, then x – 4 = 5 + 4 + 4 If n + 3 = –11, then Solving Equations
  26. 26. Sometimes an equation can be solved by adding the same number to each side or by subtracting the same number from each side or by multiplying or dividing each side by the same number. Addition and Subtraction Properties of Equality For any real numbers a , b , and c , if a = b, then a = b + c + c a = b - c - c Example: If x – 4 = 5, then x – 4 = 5 + 4 + 4 If n + 3 = –11, then n + 3 = –11 – 3 – 3 Solving Equations
  27. 27. Sometimes an equation can be solved by adding the same number to each side or by subtracting the same number from each side or by multiplying or dividing each side by the same number. Solving Equations
  28. 28. Sometimes an equation can be solved by adding the same number to each side or by subtracting the same number from each side or by multiplying or dividing each side by the same number. Multiplication and Division Properties of Equality For any real numbers a , b , and c , if a = b, then Solving Equations
  29. 29. Sometimes an equation can be solved by adding the same number to each side or by subtracting the same number from each side or by multiplying or dividing each side by the same number. Multiplication and Division Properties of Equality For any real numbers a , b , and c , if a = b, then a = b · c · c Solving Equations
  30. 30. Sometimes an equation can be solved by adding the same number to each side or by subtracting the same number from each side or by multiplying or dividing each side by the same number. Multiplication and Division Properties of Equality For any real numbers a , b , and c , if a = b, then a = b · c · c a = b Solving Equations c c
  31. 31. Sometimes an equation can be solved by adding the same number to each side or by subtracting the same number from each side or by multiplying or dividing each side by the same number. Multiplication and Division Properties of Equality For any real numbers a , b , and c , if a = b, then a = b · c · c a = b Example: Solving Equations c c
  32. 32. Sometimes an equation can be solved by adding the same number to each side or by subtracting the same number from each side or by multiplying or dividing each side by the same number. Multiplication and Division Properties of Equality For any real numbers a , b , and c , if a = b, then a = b · c · c a = b Example: 4 4 Solving Equations c c
  33. 33. Sometimes an equation can be solved by adding the same number to each side or by subtracting the same number from each side or by multiplying or dividing each side by the same number. Multiplication and Division Properties of Equality For any real numbers a , b , and c , if a = b, then a = b · c · c a = b Example: 4 4 Solving Equations c c
  34. 34. Sometimes an equation can be solved by adding the same number to each side or by subtracting the same number from each side or by multiplying or dividing each side by the same number. Multiplication and Division Properties of Equality For any real numbers a , b , and c , if a = b, then a = b · c · c a = b Example: 4 4 Solving Equations c c - 3 -3
  35. 35. Java Applet – Solving Functions End of Lesson
  36. 36. Credits PowerPoint created by Using Glencoe’s Algebra 2 text, © 2005 Robert Fant

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