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2-4 Equations and Their Solutions Warm Up Problem of the Day Lesson Presentation Lesson Quizzes 2-4 Equations and Their Solutions Warm Up Evaluate each expression for x = 8. 1. 3x + 5 29 2. x + 8 16 3. 2x – 7 9 4. 8x 4 16 5. 7x – 1 55 6. x – 3 5 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. 9 2 10 8 7 6 4 12 5 2-4 Equations and Their Solutions Learn to determine whether a number is a solution of an equation. 2-4 Equations and Their Solutions Vocabulary equation solution 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 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. s + 15 = 27 s = 12 12 + 15 s = 10 27 s = 12 is a solution because 12 + 15 = 27. 10 + 15 27 s = 10 is not a solution because 10 + 15 27. 2-4 Equations and Their Solutions Reading Math The symbol means “is not equal to.” 2-4 Equations and Their Solutions Additional Example 1A: Determining Solutions of Equations Determine whether the given value of the variable is a solution. b — 447 = 1,203 for b = 1,650 b — 447 = 1,203 ? 1,650 — 447 = 1,203 ? 1,203 = 1,203 1,203 1,203 Substitute 1,650 for b. Subtract. Because 1,203 = 1,203, 1,650 is a solution to b — 447 = 1,203. 2-4 Equations and Their Solutions Additional Example 1B: Determining Solutions of Equations Determine whether the given value of the variable is a solution. 27x = 1,485 for x = 54 27x = 1,485 ? 27 54 = 1,485 ? 1,458 = 1,485 1,458 1,485 Substitute 54 for x. Multiply. Because 1,458 1,485, 54 is not a solution to 27x = 1,485. Equations and Their Solutions 2-4 Check It Out: Example 1A Determine whether the given value of the variable is a solution. u + 56 = 139 for u = 73 u + 56 = 139 ? 73 + 56 = 139 ? 129 = 139 129 139 Substitute 73 for u. Add. Because 129 139, 73 is not a solution to u + 56 = 139. Equations and Their Solutions 2-4 Check It Out: Example 1B Determine whether the given value of the variable is a solution. 45 g = 3 for g = 15 45 g = 3 ? 45 15 = 3 Substitute 15 for g. ? Divide. 3=3 3 3 Because 3 = 3, 15 is a solution to 45 g = 3. 2-4 Equations and Their Solutions Reading Math 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. 2-4 Equations and Their Solutions Additional Example 2 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. 36 yd = in. ? 36 19 = 664 ? 684 = 664 Substitute. Multiply. Because 684 664, 19 yards is not equal to 664 inches. 2-4 Equations and Their Solutions Check It Out: Example 2 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. 12 ft = in. ? 12 7 = 84 ? 84 = 84 Substitute. Multiply. Because 84 = 84, 7 feet is equal to 84 inches. 2-4 Equations and Their Solutions Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems 2-4 Equations and Their Solutions Lesson Quiz Determine whether the given value of each variable is a solution. 1. 85 = 13x for x = 5 no 2. w + 38 = 210 for w = 172 yes 3. 8y = 88 for y = 11 yes 4. 16 = w 6 for w = 98 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.) no 2-4 Equations and Their Solutions Lesson Quiz for Student Response Systems 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 2-4 Equations and Their Solutions Lesson Quiz for Student Response Systems 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 2-4 Equations and Their Solutions Lesson Quiz for Student Response Systems 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 2-4 Equations and Their Solutions Lesson Quiz for Student Response Systems 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 2-4 Equations and Their Solutions Lesson Quiz for Student Response Systems 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