1. 2-4 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. 2-4 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. 2-4 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. 2-4 Equations and Their Solutions Learn to determine whether a number is a solution of an equation.

5. 2-4 Equations and Their Solutions equation solution Vocabulary

6. 2-4 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. 2-4 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. 2-4 Equations and Their Solutions The symbol  means “is not equal to.” Reading Math

9. 2-4 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. 2-4 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. 2-4 Equations and Their Solutions Determine whether the given value of the variable is a solution. u + 56 = 139 for u = 73 Because 129  139, 73 is not a solution to u + 56 = 139. u + 56 = 139 Substitute 73 for u. 129 = 139 ? 73 + 56 = 139 ? Check It Out: Example 1A 129 139 Add.

12. 2-4 Equations and Their Solutions Determine whether the given value of the variable is a solution. 45  g = 3 for g = 15 Because 3 = 3, 15 is a solution to 45  g = 3. 45  g = 3 Substitute 15 for g. 3 = 3 ? 45  15 = 3 ? Check It Out: Example 1B 3 3 Divide.

13. 2-4 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

14. 2-4 Equations and Their Solutions Paulo says that his yard is 19 yards long. Jamie says that Paulo’s yard 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 ?

15. 2-4 Equations and Their Solutions 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. Because 84 = 84, 7 feet is equal to 84 inches. Substitute. 84 = 84 ? 12  7 = 84 ? Check It Out: Example 2 12  ft = in. Multiply.

16. 2-4 Equations and Their Solutions Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems

17. 2-4 Equations and Their Solutions Determine whether the given value of each variable is a solution. 1. 85 = 13x for x = 5 2. w + 38 = 210 for w = 172 3. 8y = 88 for y = 11 4. 16 = w  6 for w = 98 Lesson Quiz no yes no 5. The local pizza shop charged Kylee $172 for 21 medium pizzas. The price of a medium pizza is $8. Determine whether Kylee paid the correct amount of money. (Hint: $8 pizzas = total cost.)

18. 2-4 Equations and Their Solutions 1. Identify the value of the variable that is the solution of the 9z = 63. A. z = 17 B. z = 14 C. z = 54 D. z = 72 Lesson Quiz for Student Response Systems

19. 2-4 Equations and Their Solutions 2. Identify the value of the variable that is the solution of the equation x – 125 = 375. A. x = 3 B. x = 250 C. x = 490 D. x = 500 Lesson Quiz for Student Response Systems

20. 2-4 Equations and Their Solutions 3. Identify the value of the variable that is the solution of the equation 48 = 6w. A. w = 8 B. w = 42 C. w = 54 D. w = 288 Lesson Quiz for Student Response Systems

21. 2-4 Equations and Their Solutions 4. Identify the value of the variable that is the solution of the equation k  7 = 13. A. k = 6 B. k = 20 C. k = 71 D. k = 91 Lesson Quiz for Student Response Systems

22. 2-4 Equations and Their Solutions 5. The saleswoman at a bakehouse charged Deborah $64 for 16 burgers. The price of burger is $4. Determine whether Deborah paid the correct amount of money. A. yes; the cost of 16 burgers is $64 B. no; the cost of 16 burgers is $60 C. no; the cost of 16 burgers is $58 D. no; the cost of 16 burgers is $56 Lesson Quiz for Student Response Systems