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2-10

Equations and Their Solutions. 2-10. Course 2. Warm Up. Problem of the Day. Lesson Presentation. Equations and Their Solutions. 2-10. Course 2. Warm Up Evaluate each expression for x = 12. 1. x + 2 2. 3. x – 8 4. 10 x – 4 5. 2 x + 12 6. 5 x + 7. 14. x 4. 3. 4. 116.

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2-10

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

  2. Equations and Their Solutions 2-10 Course 2 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 x 4 3 4 116 36 67

  3. Equations and Their Solutions 2-10 Course 2 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

  4. Equations and Their Solutions 2-10 Course 2 Learn to determine whether a number is a solution of an equation.

  5. Equations and Their Solutions 2-10 Course 2 Insert Lesson Title Here Vocabulary equation solution

  6. Equations and Their Solutions 2-10 Course 2 Nicole has 82 CDs. This is 9 more than her friend Jessica has. This situation can be written as an equation. An equationis a mathematical statement that two expressions are equal in value. An equation is like a balanced scale. Number of CDs Nicole has 82 is equal to = 9 more than Jessica has j + 9 Left expression Right expression

  7. Equations and Their Solutions 2-10 Course 2 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 7 + 3 = 10. 12 = t + 9 t = 4 is not a solution because 12 ≠ 4 + 9. Reading Math The symbol ≠ means “is not equal to.”

  8. Equations and Their Solutions 2-10 ? 26 + 9 = 17 ? 35 = 17 Course 2 Additional Example 1A: Determining Whether a Number is a Solution of an Equation Determine whether each number is a solution of t + 9= 17. A. 26 t + 9= 17 Substitute 26 for t.  26 is not a solution of t + 9 = 17.

  9. Equations and Their Solutions 2-10 ? 8 + 9 = 17 ? 17 = 17 Course 2 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. 8 t + 9= 17 Substitute 8 for t.  8 is a solution of t + 9 = 17.

  10. Equations and Their Solutions 2-10 ? 22– 5 = 12 ? 17 = 12 ? 8– 5 = 12 ? 3 = 12 Course 2 Insert Lesson Title Here Try This: Example 1A &1B Determine whether each number is a solution of x– 5= 12. A. 22 x– 5= 12 Substitute 22 for x.  22 is not a solution of x– 5 = 12. B. 8 x – 5= 12 Substitute 8 for x.  8 is not a solution of x– 5 = 12.

  11. Equations and Their Solutions 2-10 ? 84 = 96 + 12 ? 84 = 108 ? 84 = 72 + 12 ? 84 = 84 Course 2 Additional Example 2: Sports Application 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? 96 points 84 = h + 12 Substitute 96 for h.  72 points 84 = h + 12 Substitute 72 for h.  The Hawks scored 72 points.

  12. Equations and Their Solutions 2-10 ? 34 = 43 + 9 ? 34 = 52 ? 34 = 25 + 9 ? 34 = 34 Course 2 Insert Lesson Title Here 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? 43 items 34 = e + 9 Substitute 43 for e.  25 items 34 = e + 9 Substitute 25 for e.  Billy found 25 items.

  13. Equations and Their Solutions 2-10 ? 52 – 17 = 32 ? 35 = 32 Course 2 Additional Example 3: Writing an Equation to Determine Whether a Number is a Solution 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? If x represents the amount of money she had before she went shopping, then x – 17 = 32. $52 x – 17 = 32 Substitute 52 for x. 

  14. Equations and Their Solutions 2-10 ? 49 – 17 = 32 ? 32 = 32 Course 2 Additional Example 3 Continued $49 x – 17 = 32 Substitute 49 for x.  Mrs. Jenkins had $49 before she went shopping.

  15. Equations and Their Solutions 2-10 ? 31 + 13 = 42 ? 44 = 42 Course 2 Insert Lesson Title Here Try This: Example 3 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. 31 cards c + 13 = 42 Substitute 31 for x. 

  16. Equations and Their Solutions 2-10 ? 29 + 13 = 42 ? 42 = 42 Course 2 Insert Lesson Title Here Try This: Example 3 Continued 29 cards c + 13 = 42 Substitute 29 for c.  Matt had 29 cards before he went shopping.

  17. Equations and Their Solutions 2-10 Course 2 Insert Lesson Title Here Lesson Quiz Determine if each number is a solution of 5 + x = 47. 1.x = 42 2.x = 52 Determine if each number 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? yes no yes no 7

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