1. 2-5 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. 2-5 Equations and Their Solutions 2916 9 Warm Up Evaluate each expression for x = 8. 1. 3x + 52. x + 8 3. 2x – 74. 8x  4 5. 7x – 16. x – 3 55 5

3. 2-5 Equations and Their Solutions Problem of the Day Complete the magic square so that every row, column, and diagonal add up to the same total. 10 7 4 92 86 125

4. 2-5 Equations and Their Solutions MA.6.A.3.2 Write [and] solve…one-step linear equations… Sunshine State Standards

5. 2-5 Equations and Their Solutions equation solution Vocabulary

6. 2-5 Equations and Their Solutions An equation is a mathematical statement that two expressions are equal. You can think of a correct equation as a balanced scale. 3 + 2 5

7. 2-5 Equations and Their Solutions Equations may contain variables. If a value for a variable makes an equation true, that value is a solution of the equation. 12 + 15 27 s + 15 = 27 s = 12s = 10 10 + 15 27 s = 12 is a solution because 12 + 15 = 27. s = 10 is not a solution because 10 + 15  27.

8. 2-5 Equations and Their Solutions The symbol  means “is not equal to.” Reading Math

9. 2-5 Equations and Their Solutions Determine whether the given value of the variable is a solution. Additional Example 1A: Determining Solutions of Equations b — 447 = 1,203 for b = 1,650 Because 1,203 = 1,203, 1,650 is a solution to b — 447 = 1,203. b — 447 = 1,203 Substitute 1,650 for b. 1,203 = 1,203 ? 1,650 — 447 = 1,203 ? 1,203 Subtract.

10. 2-5 Equations and Their Solutions Determine whether the given value of the variable is a solution. Additional Example 1B: Determining Solutions of Equations 27x = 1,485 for x = 54 Because 1,458  1,485, 54 is not a solution to 27x = 1,485. 27x = 1,485 Substitute 54 for x. 1,458 = 1,485 ? 27  54 = 1,485 ? 1,458 1,485 Multiply.

11. 2-5 Equations and Their Solutions Check It Out : 1A A. u + 56 = 139 for u = 73 73 + 56 = 129, not 139; Determine whether the given value of the variable is a solution. 73 is not a solution to u + 56 = 139.

12. 2-5 Equations and Their Solutions Check It Out : 1B B. 45 = 100 - v for v = 55 100 - 55 = 45; Determine whether the given value of the variable is a solution. 55 is a solution.

13. 2-5 Equations and Their Solutions Check It Out : 1C C. 26x = 13 for x = 2 26 × 2 = 52, not 13; Determine whether the given value of the variable is a solution. 2 is not a solution.

14. 2-5 Equations and Their Solutions An equation has an equal sign, but an expression does not. An equation can be solved, but an expression can only be evaluated or simplified. Reading Math

15. 2-5 Equations and Their Solutions Paulo says that the park is 19 yards long. Jamie says that the park is 664 inches long. Determine if these two measurements are equal. Additional Example 2 Because 684  664, 19 yards is not equal to 664 inches. Substitute. 684 = 664 ? Multiply. 36  yd = in. 36  19 = 664 ?

16. 2-5 Equations and Their Solutions Check It Out : 2A Anna says that the table is 7 feet long. John says that the table is 84 inches long. Determine if these two measurements are equal. Yes; there are 12 inches in a foot, and 7 × 12 = 84. 7 feet is equal to 84 inches. Determine whether the given value of the variable is a solution.

17. 2-5 Equations and Their Solutions Check It Out : 2B Ten Museum Park is a skyscraper in Miami, Florida. It is 585 feet tall. Jerry says that its height is 195 yards. Is Jerry correct? Yes. There are 3 feet in 1 yard, and 585 ÷ 3 = 195. 585 feet is equal to 195 yards. Determine whether the given value of the variable is a solution.

18. 2-5 Equations and Their Solutions Check It Out : 2C Ralph pays $2 for an individual slice of Pizza. He can buy the entire 8-slice pizza for $12. Is this what he would pay for 8 individual slices? No; 8 × 2 = 16, so 8 individuals slices would cost $16. Determine whether the given value of the variable is a solution.

19. 2-5 Equations and Their Solutions Check It Out: 2 continued D. An Olympiad is a period of 4 consecutive years. The Olympiads are numbered consecutively from the first Olympiad which began in 1896. Which Olympiad began on the first day of 2008? Explain. 29th Olympiad; 2008 - 1896 = 112, and = 28, so 28 Olympiads were completed in that time span. 112 4