1. 1-9 Equations and Their Solutions Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes

2. 1-9 Equations and Their Solutions Warm Up Evaluate each expression for x = 12. 1. x + 2 2. 3. x – 8 4. 10x – 4 5. 2x + 12 6. 5x + 7 14 3 4 x4x4 116 36 67

3. 1-9 Equations and Their Solutions Problem of the Day Alicia buys buttons at a cost of 8 for $20. She resells them for $5 each. How many buttons does Alicia need to sell for a profit of $120? 48 buttons

4. 1-9 Equations and Their Solutions Learn to determine whether a number is a solution of an equation.

5. 1-9 Equations and Their Solutions Vocabulary equation solution

6. 1-9 Equations and Their Solutions Ella has 22 CDs. This is 9 more than her friend Kay has. This situation can be written as an equation. An equation is a mathematical statement that two expressions are equal in value. An equation is like a balanced scale. Right expressionLeft expression Number of CDs Ella has 22 is equal to = 9 more than Kay has j + 9

7. 1-9 Equations and Their Solutions Just as the weights on both sides of a balanced scale are exactly the same, the expressions on both sides of an equation represent exactly the same value. When an equation contains a variable, a value of the variable that makes the statement true is called a solution of the equation. 22 = j + 9 j = 13 is a solution because 22 = 13 + 9. 22 = j + 9 j = 15 is not a solution because 22  15 + 9. The symbol ≠ means “is not equal to.” Reading Math

8. 1-9 Equations and Their Solutions Determine whether the given value of the variable is a solution of t + 9 = 17. Additional Example 1A: Determining Whether a Number is a Solution of an Equation 26 26 + 9 = 17 ? 35 = 17 ? 26 is not a solution of t + 9 = 17.  Substitute 26 for t. t + 9 = 17

9. 1-9 Equations and Their Solutions Additional Example 1B: Determining Whether a Number is a Solution of an Equation Determine whether the given value of the variable is a solution of t + 9 = 17. 8 8 + 9 = 17 ? 17 = 17 ? 8 is a solution of t + 9 = 17. Substitute 8 for t. t + 9 = 17

10. 1-9 Equations and Their Solutions Check It Out: Example 1 Determine whether each number is a solution of x – 5 = 12. A. 22 22 – 5 = 12 ? 17 = 12 ? 22 is not a solution of x – 5 = 12.  Substitute 22 for x. B. 8 8 – 5 = 12 ? 3 = 12 ? 8 is not a solution of x – 5 = 12. Substitute 8 for x. x – 5 = 12 

11. 1-9 Equations and Their Solutions Mrs. Jenkins had $32 when she returned home from the supermarket. If she spent $17 at the supermarket, did she have $52 or $49 before she went shopping? Additional Example 2: Writing an Equation to Determine Whether a Number is a Solution $52 m – 17 = 32 52 - 17 = 32 ? 35 = 32 ?  Substitute 52 for m. You can write an equation to find the amount of money Mrs. Jenkins had before she went shopping. If m represents the amount of money she had before she went shopping, then m - 17 = 32.

12. 1-9 Equations and Their Solutions Additional Example 2 Continued $49 m – 17 = 32 49 - 17 = 32 ? 32 = 32 ? Substitute 49 for m. You can write an equation to find the amount of money Mrs. Jenkins had before she went shopping. If m represents the amount of money she had before she went shopping, then m - 17 = 32. Mrs. Jenkins had $49 before she went shopping. Mrs. Jenkins had $32 when she returned home from the supermarket. If she spent $17 at the supermarket, did she have $52 or $49 before she went shopping?

13. 1-9 Equations and Their Solutions Mr. Rorke had $12 when he returned home from buying a hat. If he spent $47 at the hat store, did he have $61 or $59 before he bought the hat? Check It Out: Example 2 $61 m – 47 = 12 61 - 47 = 12 ? 14 = 12 ? Substitute 61 for h. You can write an equation to find the amount of money Mr. Rorke had before he purchased a hat. If m represents the amount of money he had before he purchased a hat, then m – 47 = 12. 

14. 1-9 Equations and Their Solutions Mr. Rorke had $12 when he returned home from buying a hat. If he spent $47 at the hat store, did he have $59 or $61 before he bought the hat? Check It Out: Example 2 Continued $59 m – 47 = 12 59 - 47 = 12 ? 12 = 12 ? Substitute 59 for h. You can write an equation to find the amount of money Mr. Rorke had before he purchased a hat. If m represents the amount of money he had before he purchased a hat, then m – 47 = 12. Mr. Rorke had $59 before he purchased a hat.

15. 1-9 Equations and Their Solutions Which problem situation best matches the equation 5 + 2x = 13? Additional Example 3: Deriving a Real-World Situation from an Equation Situation A: Admission to the county fair costs $5 and rides cost $2 each. Mike spent a total of $13. How many rides did he go on? $2 per ride 2x Mike spent $13 in all, so 5 + 2x = 13. Situation A matches the equation. $5 for admission 5 +

16. 1-9 Equations and Their Solutions Which problem situation best matches the equation 5 + 2x = 13? Additional Example 3 Continued Situation B: Admission to the county fair costs $2 and rides cost $5 each. Mike spent a total of $13. How many rides did he go on? $5 per ride 5x Since 5x is not a term in the given equation, Situation B does not match the equation. The variable x represents the number of rides that Mike bought.

17. 1-9 Equations and Their Solutions Which problem situation best matches the equation 13 + 4x = 25? Check It Out: Example 3 Situation A: Admission to the baseball game costs $4 and souvenir hats cost $13 each. Trina spent a total of $25. How many souvenir hats did she buy? $13 per souvenir hat 13x Since 13x is not a term in the given equation, Situation A does not match the equation. The variable x represents the number of souvenir hats Trina bought.

18. 1-9 Equations and Their Solutions Which problem situation best matches the equation 13 + 4x = 25? Check It Out: Example 3 Continued Situation B: $4 per souvenir hat 4x Trina spent $25 in all, so 13 + 4x = 25. Situation B matches the equation. $13 for admission 13 + Admission to the baseball game costs $13 and souvenir hats cost $4 each. Trina spent a total of $25. How many souvenir hats did she buy?

19. 1-9 Equations and Their Solutions Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems

20. 1-9 Equations and Their Solutions Lesson Quiz Determine whether the given value of the variable is a solution of 5 + x = 47. 1. x = 42 2. x = 52 Determine whether the given value of the variable is a solution of 57 – y = 18. 3. y = 75 4. y = 39 5. Kwan has 14 marbles. This is 7 more than Drue has. Does Drue have 21 or 7 marbles? no yes no yes 7

21. 1-9 Equations and Their Solutions 1. Identify the value of the variable that is a solution of 7 + x = 52. A. x = 45 B. x = 55 C. x = 50 D. x = 60 Lesson Quiz for Student Response Systems

22. 1-9 Equations and Their Solutions 2. Identify the value of the variable that is a solution of 8 + z = 53. A. z = 57 B. z = 49 C. z = 53 D. z = 45 Lesson Quiz for Student Response Systems

23. 1-9 Equations and Their Solutions 3. Identify the value of the variable that is a solution of 71 – n = 11. A. n = 40 B. n = 60 C. n = 50 D. n = 70 Lesson Quiz for Student Response Systems

24. 1-9 Equations and Their Solutions 4. Identify the value of the variable that is a solution of 50 – y = 9. A. y = 41 B. y = 52 C. y = 48 D. y = 59 Lesson Quiz for Student Response Systems

25. 1-9 Equations and Their Solutions 5. Rita has 18 storybooks. This is nine more than Reena has. Does Reena have 3, 9, 18, or 27 storybooks? A. 27 storybooks B. 18 storybooks C. 9 storybooks D. 3 storybooks Lesson Quiz for Student Response Systems