Bellwork Sept. 22, 2010 Have homework out on desk pg. 9 in workbook  Define and give an example of each: 1. variable 2. coefficient 3. Algebraic expression 4. like terms 5. operations

1-10 Equations and Their Solutions

Essential Question  How is understanding variables useful in evaluating equations?

Definitions equation- a mathematical expression that shows that two expressions are equivalent solution- a value or values that make an equation true

Ella has 22 CDs. This is 9 more than her friend Kay has. This situation can be written as an equation. An equation is like a balanced scale. Number of CDs Ella has 22 is equal to = 9 more than Kay has j + 9 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.

22 = j + 9 j = 1322 = j + 9 j = 15 The symbol ≠ means “is not equal to.” Reading Math Number of CDs Ella has 22 is equal to = 9 more than Kay has j + 9 is a solution because 22 = is not a solution because 22 

Determine whether the given value of the variable is a solution of t + 9 = 17. Example = ≠ is not a solution of t + 9 = 17. t + 9 = 17

Example 1 continued Determine whether the given value of the variable is a solution of t + 9 = = = 17 8 is a solution of t + 9 = 17. t + 9 = 17

Example 2 Determine whether each number is a solution of x – 5 = 12. A – 5 = ≠ is not a solution of x – 5 = 12.  B. 8 8 – 5 = 12 3 ≠ 12 8 is not a solution of x – 5 = 12. x – 5 = 12 

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? Example 3 $52 m – 17 = = ≠ 32  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. $49 m – 17 = = = 32 Mrs. Jenkins had $49 before she went shopping.

Which problem situation best matches the equation 5 + 2x = 13? Example 4 Situation A: 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 A does not match the equation. The variable x represents the number of rides that Mike bought.

Which problem situation best matches the equation 5 + 2x = 13? Example 4 Situation B: 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 B matches the equation. $5 for admission 5 +

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? Example 5 $61 m – 47 = = ≠ 12 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.  $59 m – 47 = = = 12 Mr. Rorke had $59 before he purchased a hat.

Work Session  Page 48  Questions 1-5

19 = ≠27 6(13) = = ÷ 3 = = 14

25 = x = = = ≠ 29 The book Mavis wants to buy is $34.

Situation A: $2 per pound = 2x laundry detergent = $10 total = $16 Situation B: $10 per pound = 10x laundry detergent = $2 total = $16 Angie spent $16 in all, so x = 16. Situation A matches the equation.

Closing Determine whether the given value of the variable is a solution of 5 + x = x = x = 52 Determine whether the given value of the variable is a solution of 57 – y = y = y = Kwan has 14 marbles. This is 7 more than Drue has. Does Drue have 21 or 7 marbles? no yes no yes 7

Homework  Workbook  page 10  All problems

Extra Practice Evaluate each expression for x = x x – x – x x x4x