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Copyright © Ed2Net Learning, Inc.1 Good Afternoon! Today we will be learning about Solving Multi-Step Equations Lets warm up : 2) 4a + 3 = 27 1) 3x - 5 = 10 3) y + 3 = 6 7 4) m - 3 = 9 5 Simplify: 1) x = 3 2) a = 6 3) y = 21 4) m = 60

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Copyright © Ed2Net Learning, Inc. 2 Lets review with Solving 2-Step Equations "Linear" equations are mathematical expressions that have an equal sign and linear expressions However, variable(s) in linear equations: Cannot have exponents (or powers) For example, x squared or x 2 Cannot multiply or divide each other For example: "x" times "y" or xy; "x" divided by "y" or x/y Cannot be found under a root sign or square root sign (sqrt) For example: Ö x or the "square root of x"; sqrt (x)

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Copyright © Ed2Net Learning, Inc. 3 It takes two steps to solve an equation or inequality that has more than one operation: 1)Simplify using the inverse of addition or subtraction. 2)Simplify further by using the inverse of multiplication or division. When you multiply or divide an inequality by a negative number, you must reverse the inequality symbol. Review

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Copyright © Ed2Net Learning, Inc. 4 Solve 2x + 1 = 5 You can solve the problem with the help of algebra tiles. 2x + 1 = 5 2x + 1 – 1 = 5 – 1 2x = 4 2 2 x = 2 Model the equation. Remove 1 tile from each side. Divide each side into two equal groups. Simplify. Review

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Copyright © Ed2Net Learning, Inc. 5 To solve a two-step equation, first undo addition or subtraction. Then undo multiplication or division. Solve 3x – 6 = 15. Check your solution. 3x – 6 = 15 3x – 6 + 6 = 15 + 6 3x = 21 3 3 x = 7 Add 6 to each side. Divide each side by 3. Simplify. Review

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Copyright © Ed2Net Learning, Inc. 6 Check: 3x – 6 = 15 3(7) – 6 = 15 21 – 6 = 15 15 = 15 Replace x with 7. Multiply. Simplify. Review

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Copyright © Ed2Net Learning, Inc. 7 Solve x - 19 = 17. 4 Check your solution. x - 19 = 17 4 x - 19 + 19 = 17 + 19 4 x = 36 4 4. x = 4. 36 4 x = 144 Add to undo the subtraction. Multiply to undo the division. Review

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Copyright © Ed2Net Learning, Inc. 8 Check: x - 19 = 17 4 144 - 19 = 17 4 36 - 19 = 17 17 = 17 Replace x with 144. Do the division first. The solution is 144. Review

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Copyright © Ed2Net Learning, Inc. 9 Five children and one adult went to a concert. Adult tickets were $14. The total price for all the tickets was $59. What was the cost of each childs ticket? Let the cost of 1 ticket for a child is = x Total price for the tickets for five children and one adult = $59, Hence, Adult tickets were = $14 5x + 14 = 59 5x + 14 – 14 = 59 – 14 5x = 45 5 5 x = 9 Subtract to undo the addition. Divide to undo the multiplication.

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Copyright © Ed2Net Learning, Inc. 10 Negative Coefficients Solve 5 – x = 17. 5 – x = 17 -5 + 5 – x = - 5 + 17 0 – x = 12 –x = 12 -1(–x) = -1(12) x = -12 Add -5 to each side. Multiply each side by -1. Simplify. 0 – x = -x Review

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Copyright © Ed2Net Learning, Inc. 11 Lets start with Solving Multi-Step Equations Most linear equations require more than one step for their solution. Just as with solving one-step or two-step or any equation, one goal in solving an equation is to have only variables on one side of the equal sign and numbers on the other side of the equal sign. The other goal is to have the number in front of the variable (i.e., coefficient) equal to one.

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Copyright © Ed2Net Learning, Inc. 12 Steps for solving a Multi-step Equation: Step1: Use the Distributive Property wherever necessary. Step2: Combine like terms. Step3: Undo addition or subtraction. Step4: Undo multiplication or division.

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Copyright © Ed2Net Learning, Inc. 13 Solve 2x + 5 + x = 14 You can solve the problem with the help of algebra tiles. Group the tiles so that all the x tiles are together. 2x + 5 + x = 14 3x + 5 = 14 Next slide.

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Copyright © Ed2Net Learning, Inc. 14 Remove 5 tiles from each side. Divide each side into three equal groups. Simplify. 3x = 9 3 3 x = 3

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Copyright © Ed2Net Learning, Inc. 15 Now you try! 1) 8x + 4x = 144 Solve: 2) 9x - 2x = -42 1) x = 12 2) x = -6

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Copyright © Ed2Net Learning, Inc. 16 Solve: 2(5x - 3) = 14 2(5x - 3) = 14 10x - 6 = 14 10x - 6 + 6 = 14 + 6 10x = 20 10 10 x = 2 Use the Distributive property. Add 6 to each side. Divide each side by 10. Simplify. You may need to use the Distributive property when you solve a multi-step equation.

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Copyright © Ed2Net Learning, Inc. 17 Solve: 38 = -3(4y + 2) + y 38 = -3(4y + 2) + y 38 = - 12y - 6 + y 38 = - 12y + y - 6 38 = - 11y - 6 38 + 6 = - 11y - 6 + 6 44 = - 11y -11 -11 -4 = y Use the Distributive property. Add 6 to each side. Divide each side by -11. Simplify. Use the Commutative and Associative properties of addition to group like terms. Combine like terms.

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Copyright © Ed2Net Learning, Inc. 18 Now you try! 1) -3(m - 6) = 3 Solve: 2) 3(x + 12) - x = 8 1) m = 5 2) x = -14

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Copyright © Ed2Net Learning, Inc. 19 Real world problems Jake and Suki collect model airplanes. Suki has four fewer than twice as many model airplanes as Jake. Together they have 14 models. Solve the equation m + 2m - 4 = 14. Find the number of models each person has. m + 2m - 4 = 14 3m - 4 = 14 3m - 4 + 4 = 14 + 4 3m = 18 3 3 m = 6 Add 4 to each side. Divide each side by 3. Simplify. Combine like terms.

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Copyright © Ed2Net Learning, Inc. 20 Finding consecutive integers The sum of three consecutive integers is 96. Find the integers. Sum of three consecutive integers = 96 Let, n = the least integer. Then n + 1 = the second integer. And n + 2 = the third integer. Hence, the equation is: n + (n + 1) + (n + 2) = 96 Next slide.

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Copyright © Ed2Net Learning, Inc. 21 n + (n + 1) + (n + 2) = 96 (n + n+ n) + (1 + 2) = 96 3n + 3 = 96 3n + 3 - 3 = 96 - 3 3n = 93 3 3 n = 31 Solution Subtract 3 from each side. Divide each side by 3. Simplify. Combine like terms. Use the Commutative and Associative properties of addition to group like terms.

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Copyright © Ed2Net Learning, Inc. 22 Now you try! 1) The sum of four consecutive integers is 358. Find the integers. 1) 88, 89, 90, 91

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Copyright © Ed2Net Learning, Inc. 23 BREAK

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Copyright © Ed2Net Learning, Inc. 24 GAME Click on the link below for some exciting puzzle http://www.thekidzpage.com/onlinejigsawpuzzles/kids- jigsaw-puzzles/12-piece-jigsaw/11-16-06- snowgirl.html

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Copyright © Ed2Net Learning, Inc. 25 Solve each equation: 1) 5b + 11 -2b = 50 2) 4a + 1 - a = 19 3) 18 = b - 7b 4) 4d + 2d - 3d = 27 1) b = 13 2) a = 6 3) b = -3 4) d = 9 Assignment

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Copyright © Ed2Net Learning, Inc. 26 Solve each equation: 5) 3(n - 2 ) = 36 6) 4(y - 1 ) = 36 7) 2(8 + n) = 22 8) -2(a + 3) - a = 0 5) n = 14 6) y = 10 7) n = 3 8) a = 3

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Copyright © Ed2Net Learning, Inc. 27 10) The sum of three consecutive even integers is 60. Find the integers. 9) The sum of two consecutive integers is 131. Find the integers. 9) 65, 66 10) 19, 20, 21

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Copyright © Ed2Net Learning, Inc. 28 11) One basketball team defeated another by 13 points. The total number of points scored by both teams was 171 to find the number of points p scores by the winning team? 11) 92

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Copyright © Ed2Net Learning, Inc. 29 Steps for solving a Multi-step Equation: Step1: Use the Distributive Property wherever necessary. Step2: Combine like terms. Step3: Undo addition or subtraction. Step4: Undo multiplication or division. Lets review Solving Multi-Step Equations

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Copyright © Ed2Net Learning, Inc. 30 Solve 2x + 5 + x = 14 You can solve the problem with the help of algebra tiles. Group the tiles so that all the x tiles are together. 2x + 5 + x = 14 3x + 5 = 14 Next slide. Review

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Copyright © Ed2Net Learning, Inc. 31 Remove 5 tiles from each side. Divide each side into three equal groups. Simplify. 3x = 9 3 3 x = 3 Review

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Copyright © Ed2Net Learning, Inc. 32 Solve: 2(5x - 3) = 14 2(5x - 3) = 14 10x - 6 = 14 10x - 6 + 6 = 14 + 6 10x = 20 10 10 x = 2 Use the Distributive property. Add 6 to each side. Divide each side by 10. Simplify. You may need to use the Distributive property when you solve a multi-step equation. Review

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Copyright © Ed2Net Learning, Inc. 33 Solve: 38 = -3(4y + 2) + y 38 = -3(4y + 2) + y 38 = - 12y - 6 + y 38 = - 12y + y - 6 38 = - 11y - 6 38 + 6 = - 11y - 6 + 6 44 = - 11y -11 -11 -4 = y Use the Distributive property. Add 6 to each side. Divide each side by -11. Simplify. Use the Commutative and Associative properties of addition to group like terms. Combine like terms. Review

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Copyright © Ed2Net Learning, Inc. 34 Real world problems Jake and Suki collect model airplanes. Suki has four fewer than twice as many model airplanes as Jake. Together they have 14 models. Solve the equation m + 2m - 4 = 14. Find the number of models each person has. m + 2m - 4 = 14 3m - 4 = 14 3m - 4 + 4 = 14 + 4 3m = 18 3 3 m = 6 Add 4 to each side. Divide each side by 3. Simplify. Combine like terms. Review

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Copyright © Ed2Net Learning, Inc. 35 Finding consecutive integers The sum of three consecutive integers is 96. Find the integers. Sum of three consecutive integers = 96 Let, n = the least integer. Then n + 1 = the second integer. And n + 2 = the third integer. Hence, the equation is: n + (n + 1) + (n + 2) = 96 Next slide. Review

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Copyright © Ed2Net Learning, Inc. 36 n + (n + 1) + (n + 2) = 96 (n + n+ n) + (1 + 2) = 96 3n + 3 = 96 3n + 3 - 3 = 96 - 3 3n = 93 3 3 n = 31 Solution Subtract 3 from each side. Divide each side by 3. Simplify. Combine like terms. Use the Commutative and Associative properties of addition to group like terms. Review

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Copyright © Ed2Net Learning, Inc. 37 You have done a nice job. See you in the next session.

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