2-10 Equations and Their Solutions Course 2 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

Warm Up Evaluate each expression for x = x x – x – x x Course Equations and Their Solutions x4x

Problem of the Day Alicia buys buttons at a cost of 8 for $20. She in turn resells them in her shop for $5 each. How many buttons does Alicia need to sell in order to make a profit of $120? 48 buttons Course Equations and Their Solutions

Learn to determine whether a number is a solution of an equation. Course Equations and Their Solutions

Vocabulary equation solution Insert Lesson Title Here Course Equations and Their Solutions

Nicole has 82 CDs. This is 9 more than her friend Jessica 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 Nicole has 82 is equal to = 9 more than Jessica has j + 9 Course 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. x + 3 = 10 x = 7 is a solution because = = t + 9 t = 4 is not a solution because 12 ≠ The symbol ≠ means “is not equal to.” Reading Math Course Equations and Their Solutions

Determine whether each number is a solution of t + 9 = 17. Additional Example 1A: Determining Whether a Number is a Solution of an Equation A = 17 ? 35 = 17 ? 26 is not a solution of t + 9 = 17.  Substitute 26 for t. t + 9 = 17 Course Equations and Their Solutions

Additional Example 1B: Determine Whether a Number is a Solution of an Equation Determine whether each number is a solution of t + 9 = 17. B = 17 ? 17 = 17 ? 8 is a solution of t + 9 = 17. Substitute 8 for t. t + 9 = 17 Course Equations and Their Solutions

Try This: Example 1A &1B Insert Lesson Title Here Determine whether each number is a solution of x – 5 = 12. A – 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  Course Equations and Their Solutions

The Bulldogs scored 84 points in a game, 12 points more than the Hawks scored. The equation 84 = h + 12 can be used to represent the number of points the Hawks scored. Did the Hawks score 96 or 72 points? Additional Example 2: Sports Application 96 points 84 = h = ? 84 = 108 ?  72 points 84 = h = ? 84 = 84 ? The Hawks scored 72 points. Substitute 96 for h. Substitute 72 for h. Course Equations and Their Solutions

Try This: Example 2 During a scavenger hunt James found 34 items, 9 more than Billy. The equation 34 = e + 9 can be used to represent the number of items James found. Did Billy find 43 items or 25 items? Insert Lesson Title Here 43 items 34 = e = ? 34 = 52 ?  25 items 34 = e = ? 34 = 34 ? Billy found 25 items. Substitute 43 for e. Substitute 25 for e. Course Equations and Their Solutions

Mrs. Jenkins had $32 when she returned home from grocery shopping. If she spent $17 at the supermarket, did she have $52 or $49 before she went shopping? Additional Example 3: Writing an Equation to Determine Whether a Number is a Solution If x represents the amount of money she had before she went shopping, then x – 17 = 32. x – 17 = 32 $52 52 – 17 = 32 ? 35 = 32 ?  Substitute 52 for x. Course Equations and Their Solutions

$49 Additional Example 3 Continued x – 17 = – 17 = 32 ? 32 = 32 ? Substitute 49 for x. Mrs. Jenkins had $49 before she went shopping. Course Equations and Their Solutions

Try This: Example 3 Insert Lesson Title Here Matt had 42 baseball cards when he returned from the store. He bought 13 new cards at the store. Did he have 29 or 31 cards before he went to the store? If c represents the number of cards he had before he went to the store, then c + 13 = 42. c + 13 = cards = 42 ? 44 = 42 ?  Substitute 31 for x. Course Equations and Their Solutions

Try This: Example 3 Continued Insert Lesson Title Here 29 cards = 42 ? 42 = 42 ? Substitute 29 for c. Matt had 29 cards before he went shopping. c + 13 = 42 Course Equations and Their Solutions

Lesson Quiz Determine if each number is a solution of 5 + x = x = x = 52 Determine if each number 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 Insert Lesson Title Here no yes 7 Course Equations and Their Solutions