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6th Grade Math: Chapter 2 LEARNING GOAL Students will understand variables, expressions, and equations by being able to do the following: • Identify and Evaluate Expressions (2-1) • Translate between Words and Math (2-2) • Determine Whether a Number is a Solution of an Equation (2-3) • Solve Whole-Number Addition Equations (2-4) • Solve Whole-Number Subtraction Equations (2-5) • Solve Whole-Number Multiplication Equations (2-6) • Solve Whole-Number Division Equations (2-7) 2-3 Equations and Their Solutions HW: Pg. 54 #8-23 ANSWERS Course 1 2-3 Course 1 Equations and Their Solutions 2-3 Equations and Their Solutions th 6 Grade Math HW Page 60 #8-20 all Course 1 2-3 Equations and Their Solutions Warm Up Problem of the Day Lesson Presentation Course Course 11 2-3 Equations and Their Solutions Warm Up Evaluate each expression for x = 8. 1. 2. 3. 4. 5. 6. Course 1 3x + 5 x+8 2x – 7 8x 4 7x – 1 x–3 29 16 9 16 55 5 Equations and Their Equations Solutions 2-3 Solving Subtraction Problem of the Day Complete the magic square so that every row, column, and diagonal add up to the same total. Course 1 9 2 10 8 7 6 4 12 5 2-3 Equations and Their Solutions Today’s Learning Goal Learn to determine whether a number is a solution of an equation. Course 1 2-3 Equations and Their Solutions Vocabulary equation solution Course 1 2-3 Equations and Their Solutions An equation is a mathematical statement that two quantities are equal. You can think of a correct equation as a balanced scale. 3+2 Course 1 5 2-3 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. Course 1 10 + 15 27 s = 10 is not a solution because 10 + 15 27. 2-3 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 Course 1 1,203 Substitute 1,650 for b. Subtract. Because 1,203 = 1,203, 1,650 is a solution to b — 447 = 1,203. 2-3 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 Course 1 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 2-3 Try This: 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. Course 1 Equations and Their Solutions 2-3 Try This: Example 1B Determine whether the given value of the variable is a solution. 45 g = 3 for g = 15 45 g = 3 ? 45 15 = 3 Substitute 15 for g. ? Divide. 3=3 3 3 Because 3 = 3, 15 is a solution to 45 g = 3. Course 1 2-3 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 y = 664 ? 36 19 = 664 ? 684 = 664 Substitute 19 for y Multiply. Because 684 664, 19 yards are not equal to 664 inches. Course 1 2-3 Equations and Their Solutions 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. 12f = 84 ? 12 7 = 84 ? 84 = 84 Substitute 7 for f. Multiply. Because 84 = 84, 7 feet is equal to 84 inches. Course 1 2-3 Equations and Their Solutions Lesson Quiz Determine whether the given value of the 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 if Kylee paid the correct amount of money. (Hint: $8 • pizzas = total cost.) no Course 1