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# 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 equation Open sentences are neither true nor false until the variables have been replaced by numbers.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 equation Open sentences are neither true nor false until the variables have been replaced by numbers.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 equation Open sentences are neither true nor false until the variables have been replaced by numbers.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