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BANK |  |  |\n| --- | --- | --- |\n| Addition Property of Equality | Subtraction Property of Equality | Division Property of Equality |\n| Associative Property | Distributive Property | Commutative Property of Addition |\n\nDirections: Solve each equation by showing each step and justify that step by  \nwriting the appropriate property from the word bank in the blank provided. 1.) Solve: 2(x + 3) + 4 = 18  \na. Apply the distributive property: 2(x + 3) becomes 2x + 6  \nEquation: 2x + 6 + 4 = 18 ___________________________________  \nb. Combine like terms using the associative/commutative property:  \n6 + 4 = 10, so 2x + 10 = 18 ___________________________________  \nc. Subtract 10 from both sides and divide by 2: x = __________  \n2.) Solve: (5 + 3x) + 4 = x + 16  \na. Reorder (5 + 3x) using the commutative property:  \n5 + 3x becomes 3x + 5    \nb. Group the constants using the associative property:  \n(3x + 5) + 4 becomes 3x + (5 + 4)    \nc. Simplify to get: 3x + 9 = x + 16  \nd. Subtract x from both sides and then subtract 9: x =    \nMashup Math LLC | Al[l Rights Reserved | Get More K-12 Math Worksheets at ](l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com)[www.mashupmath.com](l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com) 1  \n3.) Solve: 4(2x – 3) = 2(3x + 1) + 6  \na. Expand both sides using the distributive property:  \nLeft: 4(2x – 3) = 8x – 12    \nRight: 2(3x + 1) = 6x + 2, and then 6x + 2 + 6 = 6x + 8  \nb. Write the equation: 8x – 12 = 6x + 8  \nc. Subtract 6x from both sides and then add 12: x =    \n4.) Solve: (2x + 7) + (3 – x) = 10  \na. Use the commutative property to write (3 – x) as (–x + 3):  \nEquation becomes: 2x + 7 – x + 3 = 10  b. Group like terms using the associative property:  \n(2x – x) + (7 + 3) = x + 10    \nc. Isolate x by subtracting 10: x =    \n5.) Solve: 2(3x + 4)– 3(x – 2) = 5x + 10  \na. Expand using the distributive property: 2(3x + 4) = 6x + 8 and 3(x – 2) = 3x – 6 Note: Subtracting 3(x – 2) gives: –3x + 6  \nb. Combine like terms (apply the commutative property to reorder if needed):  \n6x + 8 – 3x + 6 = 3x + 14  \n___________________________________  \nc. Write the equation: 3x + 14 = 5x + 10  \nd. Subtract 3x and then subtract 10: x =    \nMashup Math LLC | Al[l Rights Reserved | Get More K-12 Math Worksheets at ](l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com)[www.mashupmath.com](l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com) 2  \n6.) Advanced Challenge: Solve: 3[2(x + 3)– 4] + 5 = 2(3x + 8)– x  \na. Inside the brackets, use the distributive property:  \n2(x + 3) = 2x + 6; then 2x + 6 – 4 = 2x + 2 ________________________________  \nb. Multiply by 3 using the distributive property: 3(2x + 2) = 6x + 6; then add 5: 6x + 11  \nc. Expand the right side:  \n2(3x + 8) = 6x + 16; then subtract x: 6x + 16 – x = 5x + 16    \nd. Set the equation: 6x + 11 = 5x + 16  \ne. Subtract 5x from both sides and then subtract 11: x =    \nMashup Math LLC | Al[l Rights Reserved | Get More K-12 Math Worksheets at ](l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com)[www.mashupmath.com](l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com) 3  \nAnswer Key  \n1.)  \na. 2(x + 3) expands to 2x + 6 → Distributive Property  \nb. 6 + 4 = 10 → Associative/Commutative Property of Addition  \nc. 2x + 10 = 18 → 2x = 8 → x = 4  \n2.)  \na. 5 + 3x becomes 3x + 5 → Commutative Property of Addition  \nb. (3x + 5) + 4 = 3x + (5 + 4) = 3x + 9 → Associative Property of Addition  \nc. 3x + 9 = x + 16 → 2x = 7 → x = 7/2  \n3.)  \na. 4(2x – 3) = 8x – 12 → Distributive Property 2(3x + 1) = 6x + 2, then 6x + 2 + 6 = 6x + 8  \nb. Equation: 8x – 12 = 6x + 8  \nc. 8x – 6x = 8 + 12 → 2x = 20 → x = 10  \n4.)  \na. Rewrite (3 – x) as (–x + 3) → Commutative Property of Addition  \nb. Group: (2x – x) + (7 + 3) = x + 10 → Associative Property of Addition  \nc. x + 10 ","cbCaiom0TXk7rbeI","https://ap.wps.com/l/cbCaiom0TXk7rbeI","pdf",765906,"English","# Word Bank\n# Directions\n# Problems\n## 1.\n## 2.\n## 3.\n## 4.\n## 5.\n## 6. Advanced Challenge\n# Answer Key","[{\"question\":\"What should students do for each equation in this worksheet?\",\"answer\":\"Solve the equation by showing every step and justify each step by writing the correct property from the word bank in the blanks.\"},{\"question\":\"Which properties are listed in the word bank?\",\"answer\":\"It includes Addition Property of Equality, Subtraction Property of Equality, Division Property of Equality, Associative Property, Distributive Property, and Commutative Property.\"},{\"question\":\"How is the distributive property used during the problems?\",\"answer\":\"It expands expressions like 2(x + 3) or 4(2x − 3) into sums such as 2x + 6 or 8x − 12, which then allows combining like terms before isolating the variable.\"}]","Using Properties to Justify Steps in Solving - Solve Equations Using Equality Properties | PDF",1790149729]