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Final Jeopardy

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RULES OF THE GAME 1. Teams of 4-5 1. 1 dry erase board, 1 marker, and 1 eraser per student 1. The teacher will pick the first question 1. The team that answers the first question correctly will then choose the next category and question 1. To get a question correct, each member of each group MUST show the work and correct answer.

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Distributive 1-side Distributive 2-side SpiroRewriteMixed 10 20 30 40 50

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Distributive 1-side 10 points Solve for x: 2(x - 2) + 8 = 12

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10 points Solve for x: 2(x - 2) + 8 = 12 2x – 4 + 8 = 12 2x + 4 = 12 2x = 8 x = 4 Distribute 2 Add -4 and 8 Subtract 4 Divide by 2

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Distributive 1-side 20 points Solve for x: 2(x + 1) + 5 = x + 2

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20 points Is x = -3 a solution? Why or why not? 2(x + 1) + 5 = x + 2 2(-3 + 1) + 5 = -3 + 2 2(-2) + 5 = -1 -4 + 5 = -1 1 ≠ -1 Right side: Insert -3 for x Add -3 and 2 Left Side: Insert -3 for x Add -3 and 1 Multiplied 2 and -2 Add -4 and 5 No, x = -3 is not a solution to the equation because 1 ≠ 1.

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Distributive 1-side 30 points Solve for x: - (3x - 2) = - 7

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30 points Distribute the - Subtract 2 Divide by - 3 Solve for x: - (3x - 2) = - 7 -3x + 2 = - 7 -3x = - 9 x = 3

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Distributive 1-side 40 points Solve for x: x + 2 + 3x = 4(x – 1)

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Solve for x: x + 2 + 3x = 4(x – 1) 4x + 2 = 4(x – 1) 4x + 2 = 4x – 4 4x = 4x - 6 No solution. 40 points Left side: Add x and 3x Subtract 2 If you subtract 4x from both sides we are left with ZERO x’s. That means there is no solution. Right side: Distribute 4

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Distributive 1-side 50 points Solve for x: 2(3x + 4) + 2 = 6x + 10

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50 points Solve for x: 2(3x + 4) + 2 = 6x + 10 6x + 8 + 2 = 6x + 10 6x + 10 = 6x + 10 6x = 6x x = x Distribute 2 Add 8 and 2 Subtract 10 Divide by 6 There are infinitely many solutions.

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Distributive 2-side 10 points Solve for m: 5(m - 1) = 2(m + 2)

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10 points Solve for m: 5(m - 1) = 2(m + 2) 5m - 5 = 2m + 4 3m - 5 = 4 3m = 9 m = 3 Left Side: Distribute 5 Add 5 Divide by 3 Right Side: Distribute 2 Subtract 2m

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Distributive 2-side 20 points Solve for x: 7(-x + 1) = 3(2x - 4)

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20 points 7(-x + 1) = 3(2x - 4) -7x + 7 = 6x -12 -13x + 7 = -12 -13x = -19 x = 19/13

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Distributive 2-side 30 points Solve for n: 7(2n – 3) = 5(3n – 4)

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14n – 21 = 15n - 20 -21 = n - 20 -1 = n 30 points Left side: Distribute 7 Subtract 14n Right side: Distribute 5 Add 20

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Distributive 2-side 40 points Solve for p: -(p + 17) = 5(p – 3)

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-p - 17 = 5p – 15 -17 = 6p – 15 -2 = 6p -2/6 = p -1/3 = p 40 points Left side: Distribute – Add p Left side: Distribute 5 Add 15 Divide by 6

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Distributive 2-side 50 points Solve for s: -(-4 + s) = -1/3(12s – 21)

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4 – s = (-12/3)s + (21/3) 4 – s = -4s + 7 4 = -3s + 7 -3 = -3s 1 = s 50 points Left side: Distribute – Add s Left side: Distribute –1/3 Simplify Subtract 7 Divide by -3

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Spiro 10 points Spiro the Spectacular chooses a number and then performs these four steps, in order. Add 3 Multiply by 2 Subtract 13 Divide by 3 If Spiro starts with 5, what is his ending number?

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Add 3 Multiply by 2 Subtract 13 Divide by 3 10 points Start with 5: 5 + 3 = 8 2(8) = 16 16 - 13 = 3 3/3 = 1

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Spiro 20 points Spiro the Spectacular chooses a number and then performs these four steps, in order. Add 3 Multiply by 2 Subtract 13 Divide by 3 Spiro says, “Wow! My ending number is 9!” Use backtracking to find his starting number.

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Add 3 Multiply by 2 Subtract 13 Divide by 3 Backtrack: Multiply by 3 Add 13 Divide by 2 Subtract 3 20 points End with 9: (9)(3) = 27 27 + 13 = 40 40/2 = 20 20 – 3 = 17

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Spiro 30 points Spiro the Spectacular chooses a number and then performs these two steps, in order. Multiply by 5 Subtract 10 Which of the following methods can Spiro use to find your starting number? 1. Divide the ending number by 5 and then add 10 or 2. Add 10 to the ending number and then divide by 5.

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30 points Starting number: 3 Multiply by 5 = (3)(5) = 15 Subtract 10 = (15-10) = 5 Ending number: 5 1. Divide the ending number by 5 and then add 10 5/5 = 1 + 10 ≠ 3 2. Add 10 to the ending number and then divide by 5. 5 + 10 = 15/5 = 3 The second one is correct.

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Spiro 40 points Spiro the Spectacular chooses a number and then performs these four steps, in order. Divide by 3 Subtract 8 Multiply by 4 Add 3 If Spiro’s starting number is n, write an expression for his ending number.

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Divide by 3 Subtract 8 Multiply by 4 Add 3 40 points Starting number: n n/3 (n/3) – 8 4((n/3) – 8) 4((n/3) – 8) +3

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Spiro 50 points Spiro the Spectacular chooses a number and then performs these four steps, in order. Divide by 6 Subtract 8 Multiply by 2 Add 3 1.If Spiro starts with 6, what is his ending number? 2.If Spiro ends with 9, what is his starting number? 3.If Spiro’s starting number is n, write an expression for his ending number. There should be 3 answers.

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Divide by 3 Subtract 8 Multiply by 2 Add 3 50 points 1. Start with 6: (6/3) = 2 2 – 8 = -6 (-6)(2) = -12 -12 + 3 = -9 2. End with 9: 9 – 3 = 6 (6/2) = 3 3 + 8 = 11 (11)(3) = 33 3. Start with n: 2((n/3) – 8) + 3 1.Follow each step. 2.Use backtracking. 3.Follow each step using n.

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Rewrite 10 points Rewrite the expression as an equivalent expression without parentheses. 3(x + 3)

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10 points 3(x + 3) = 3x + 9

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Rewrite 20 points Rewrite the expression as an equivalent expression without parentheses. 6(2x + 4)

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6(2x + 4) = 12x + 24 20 points

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Rewrite 30 points Rewrite the expression as an equivalent expression without parentheses. (1/2)(4m + 6) + 2

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(1/2)(4m + 6) + 2 = 2m + 3 + 2 = 2m + 5 30 points

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Rewrite 40 points Rewrite the expression as an equivalent expression without parentheses. (3/2)(2m + 4) + 9

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(3/2)(2m + 4) + 9 = 3m + 6 + 9 = 3m +15 40 points

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Rewrite 50 points Rewrite the expression as an equivalent expression without parentheses.

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50 points

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Random 10 points Solve for m using the number line: 5m + 6 = m + 18

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10 points mmmmm m 18 6 5m + 6 = m + 18 4m + 6 = 18 4m = 12 m = 3 Subtract 6 Divide by 4

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Random 20 points Solve the equation using squares and triangle: 5x + 6 = 3x + 10 x1

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20 points 1x 5x + 6 = 3x + 10 xx xx xxx11 111 111 1 111 111 = 2x = 4 x = 2 Divide by 2 5 triangles and 6 squares 3 triangles and 10 squares Since there are 3 triangles on the right side and 5 on the left, we can cancel out 3 of the triangles. Since there are 6 squares on the left and 10 on the right, we can cancel out 6 of the squares.

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Random 30 points Solve for x:

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30 points

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Random 40 points What is the mistake in this solution? -3(v - 8) = 5(v + 1) -3v - 24 = 5v + 5 -24 = 8v + 5 -29 = 8v -29/8 = v

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The - was not distributed properly. 40 points -3(v - 8) = 5(v + 1) -3v + 24 = 5v + 5 24 = 8v + 5 19 = 8v 19/8 = v

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Random 50 points Solve for s: 11s + 7 = 8s - 17

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50 points Solve for s: 11s + 7 = 8s - 17 3s + 7 = -17 3s = - 24 s = 8 Left side: Subtract 7 Divide by 3 Right side: Subtract 8s

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FINAL JEOPARDY Solve for x: 2(m + 3) – 4(2m + 1) = m – 3(2 + m)

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Solve for x: 2(m + 3) – 4(2m + 1) = m – 3(2 + m) 2m + 3 – 4(2m + 1) = m – 6 – 3m 2m + 3 – 8m – 4 = -2m – 6 -6m + 3 – 4 = -2m – 6 -6m – 1 = -2m – 6 -6m = -2m - 5 -4m = -5 m = -5/-4 m = 5/4 Left side: Distribute 2 Distribute -4 Subtract: 2m – 8m Subtract: 3 - 4 Add 1 Divide by -4 Right side: Distribute -3 Subtract: m – 3m Add 2m Simplify

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Example 1 Solving Two-Step Equations SOLUTION a. 12x2x + 5 = Write original equation. 112x2x + – = 15 – Subtract 1 from each side. (Subtraction property.

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