# M TH a2+b2. Works. Solving Algebraic Equations. =c 2. Time. Content. Objectives. Materials. Common Core State Standards. Teacher Notes.

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5 Name: Solving Algebraic Equations Worksheet Directions: Use the specified DECI-BLOCKS to build the balance scales for each of the following algebraic equations. Solve for the variable based on your work on the balance scale. 1. 3k = 2k + 6 DECI-BLOCKS needed: green triangles How many pairs of green triangles can you remove? k = 2. 7j 9 = 4j DECI-BLOCKS needed: black trapezoids What do you need to do with the ( 9)? How many pairs of black trapezoids can you remove? j = 3. 6p = 2p + 12 DECI-BLOCKS needed: pink trapezoids How many pairs of pink trapezoids can you remove? p = 4. 3m 8 = m DECI-BLOCKS needed: purple triangles What do you need to do with the ( 8)? How many pairs of purple triangles can you remove? m =

6 Name: Solving Algebraic Equations Worksheet Continued 5. 4s = 6s 20 DECI-BLOCKS needed: green triangles How many pairs of green triangles can you remove? What do you need to do with the ( 20)? s = 6. t + 16 = 3t DECI-BLOCKS needed: pink trapezoids How many pairs of pink trapezoids can you remove? t = 7. 3s s = 5s DECI-BLOCKS needed: purple triangles How many pairs of purple triangles can you remove? What do you need to do with the like terms? s = 8. 5n + 3 2n = 4n 2 DECI-BLOCKS needed: black trapezoids How many pairs of black trapezoids can you remove? What do you need to do with the like terms? n =

7 Name: Solving Algebraic Equations Worksheet Answer Key Directions: Use the specified DECI-BLOCKS to build the balance scales for each of the following algebraic equations. Solve for the variable based on your work on the balance scale. 18 = What is your new equation? 7j = 4j + 9 7(3) 9 = 4(3) 21 9 = = k = 2k + 6 DECI-BLOCKS needed: green triangles How many pairs of green triangles can you remove? 2 k = (6) = 2(6) = j 9 = 4j DECI-BLOCKS needed: black trapezoids What do you need to do with the ( 9)? add 9 to both sides - 9 How many pairs of black trapezoids can you remove? 4 j = p = 2p + 12 DECI-BLOCKS needed: pink trapezoids 12 = 12 How many pairs of pink trapezoids can you remove? p = 3 6(3) = 2(3) = m 8 = m DECI-BLOCKS needed: purple triangles What do you need to do with the ( 8)? add 8 to both sides What is your new equation? 3m = m How many pairs of purple triangles can you remove? 1 m = 4 3(4) 8 = = 4 4 = 4

8 Name: Solving Algebraic Equations Worksheet Answer Key Continued 5. 4s = 6s 20 DECI-BLOCKS needed: green triangles - 20 What do you need to do with the ( 20)? add 20 to both sides What is your new equation? 4s + 20 = 6s How many pairs of green triangles can you remove? 4 s = t + 16 = 3t DECI-BLOCKS needed: pink trapezoids 40 = 40 How many pairs of pink trapezoids can you remove? 1 t = = 3(8) 24 = s s = 5s DECI-BLOCKS needed: purple triangles What do you need to do with the like terms? add them What is your new equation? 4s + 4 = 5s How many pairs of purple triangles can you remove? 4 s = 4 3(4) = 5(4) = = = n + 3 2n = 4n 2 DECI-BLOCKS needed: black trapezoids What do you need to do with the like terms? subtract them What is your new equation? 3n + 3 = 4n How many pairs of black trapezoids can you remove? 3 n = 5 5(5) + 3 2(5) = 4(5) = = = 18

9 Additional Algebraic Equations and Answers Intervention Problems and Answers 1. 7p + 6 = 8p p = r = r + 9 r = z + 8 = 5z z = z = z + 9 z = h + 5 = 3h h = m = m + 7 m = f f = 7f f = r = r r + 1 r = 3 Extension Problems and Answers 1. 4y + 2 y = 5y 4 + y y = r 5 = 4r 20 r = y 5y + 3 = 8y 4y + 3 y = n + 2 4n = 4n 1 n = t 18 = 3t t t = b 8 + b = 4b 12 + b 1 b = n 20 = 3n n 6 n = g + 11 = 4g g g = 4

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