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Course 1. 2-4. Equations and Their Solutions. Warm Up. Problem of the Day. Lesson Presentation. Course 1. Warm Up Evaluate each expression for x = 8. 1. 3 x + 5 2. x + 8 3. 2 x – 7 4. 8 x  4 5. 7 x – 1 6. x – 3. 29. 16. 16. 9. 55. 5. Objective for today.

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Course 1

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  1. Course 1 2-4 Equations and Their Solutions Warm Up Problem of the Day Lesson Presentation Course 1

  2. Warm Up Evaluate each expression for x = 8. 1. 3x + 5 2.x + 8 3. 2x – 74. 8x  4 5. 7x– 1 6.x– 3 29 16 16 9 55 5

  3. Objective for today Learn to determine whether a number is a solution of an equation.

  4. Vocabulary equation solution

  5. 3 + 2 5 An equation is a mathematical statement that two quantities are equal. You can think of a correct equation as a balanced scale.

  6. 10 + 15 27 12 + 15 27 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 s = 10 s = 12 is a solution because 12 + 15 = 27. s = 10 is not a solution because 10 + 15  27.

  7. ? 1,650— 447 = 1,203 ? 1,203 1,203 1,203 = 1,203 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 Substitute 1,650 for b. Subtract. Because 1,203 = 1,203, 1,650 is a solution to b — 447 = 1,203.

  8. ? 2754 = 1,485 1,458 ? 1,485 1,458 = 1,485 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 Substitute 54 for x. Multiply. Because 1,458  1,485, 54 is not a solution to 27x = 1,485.

  9. ? 73 + 56 = 139 129 ? 139 129 = 139 Try this: Example 1A Determine whether the given value of the variable is a solution. u + 56 = 139 for u = 73 u + 56 = 139 Substitute 73 for u. Add. Because 129  139, 73 is not a solution to u + 56 = 139.

  10. ? 45  15 = 3 ? 3 3 3 = 3 Try this: Example 1B Determine whether the given value of the variable is a solution. 45  g = 3 for g = 15 45  g = 3 Substitute 15 for g. Divide. Because 3 = 3, 15 is a solution to 45  g = 3.

  11. ? 36  19 = 664 ? 684 = 664 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. Substitute. Multiply. Because 684  664, 19 yards are not equal to 664 inches.

  12. ? ? 84 = 84 12 7= 84 Try this: 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. Substitute. Multiply. Because 84 = 84, 7 feet is equal to 84 inches.

  13. Lesson Quiz 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 no yes yes no 5. The local pizza shop charged Kylee $172 for 21 medium pizzas. The price of a medium pizza is $8. Determine if Kylee paid the correct amount of money. (Hint: $8 •pizzas = total cost.) no

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