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Understanding Equations: Warm-Up and Problem Solving Lesson

Learn how to evaluate expressions and determine solutions of equations. Practice completing magic squares and checking for correct solutions. Enhance your math skills with engaging quizzes.

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Understanding Equations: Warm-Up and Problem Solving Lesson

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  1. Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

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

  3. 10 7 4 Problem of the Day Complete the magic square so that every row, column, and diagonal add up to the same total. 9 2 8 6 12 5

  4. Learn to determine whether a number is a solution of an equation.

  5. Vocabulary equation solution

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

  7. 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.

  8. Reading Math The symbol  means “is not equal to.”

  9. ? 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.

  10. ? 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.

  11. ? 73 + 56 = 139 129 ? 139 129 = 139 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 Substitute 73 for u. Add. Because 129  139, 73 is not a solution to u + 56 = 139.

  12. ? 45  15 = 3 ? 3 3 3 = 3 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 Substitute 15 for g. Divide. Because 3 = 3, 15 is a solution to 45  g = 3.

  13. 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.

  14. ? 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 is not equal to 664 inches.

  15. ? ? 84 = 84 12 7= 84 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. Substitute. Multiply. Because 84 = 84, 7 feet is equal to 84 inches.

  16. Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems

  17. 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 = 88for 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 whether Kylee paid the correct amount of money. (Hint: $8 •pizzas = total cost.) no

  18. 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

  19. Lesson Quiz for Student Response Systems 2. Identify the value of the variable that is the solution of the equationx – 125 = 375. A.x = 3 B.x = 250 C.x = 490 D.x = 500

  20. Lesson Quiz for Student Response Systems 3. Identify the value of the variable that is the solution of the equation48 = 6w. A.w = 8 B.w = 42 C.w = 54 D.w = 288

  21. 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

  22. 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

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