Using Properties to Justify Steps in Solving - Solve Equations Using Equality Properties

Sep 23, 2026

Uploaded by Bulrr

Worksheet materials for solving algebraic equations by showing each step and justifying transformations with specific properties. A word bank lists Addition/Subtraction/Division Properties of Equality plus associative, distributive, and commutative properties. Students apply distributive property for expansion, use associative/commutative to reorder and group terms, then isolate the variable through subtraction and division. Includes an advanced challenge and a separate answer key providing final solutions and property labels.

LanguageEnglish

CategoryExam

FormatPDF

Pages4

Reading Time10 min

AccessFree to download

Word Bank

Directions

Problems

6. Advanced Challenge

Answer Key

Name: ______________________________ Using Properties to Justify Steps in Solving | WORD BANK | | | | --- | --- | --- | | Addition Property of Equality | Subtraction Property of Equality | Division Property of Equality | | Associative Property | Distributive Property | Commutative Property of Addition | Directions: Solve each equation by showing each step and justify that step by writing the appropriate property from the word bank in the blank provided. 1.) Solve: 2(x + 3) + 4 = 18 a. Apply the distributive property: 2(x + 3) becomes 2x + 6 Equation: 2x + 6 + 4 = 18 ___________________________________ b. Combine like terms using the associative/commutative property: 6 + 4 = 10, so 2x + 10 = 18 ___________________________________ c. Subtract 10 from both sides and divide by 2: x = __________ 2.) Solve: (5 + 3x) + 4 = x + 16 a. Reorder (5 + 3x) using the commutative property: 5 + 3x becomes 3x + 5 b. Group the constants using the associative property: (3x + 5) + 4 becomes 3x + (5 + 4) c. Simplify to get: 3x + 9 = x + 16 d. Subtract x from both sides and then subtract 9: x = Mashup 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 3.) Solve: 4(2x – 3) = 2(3x + 1) + 6 a. Expand both sides using the distributive property: Left: 4(2x – 3) = 8x – 12 Right: 2(3x + 1) = 6x + 2, and then 6x + 2 + 6 = 6x + 8 b. Write the equation: 8x – 12 = 6x + 8 c. Subtract 6x from both sides and then add 12: x = 4.) Solve: (2x + 7) + (3 – x) = 10 a. Use the commutative property to write (3 – x) as (–x + 3): Equation becomes: 2x + 7 – x + 3 = 10 b. Group like terms using the associative property: (2x – x) + (7 + 3) = x + 10 c. Isolate x by subtracting 10: x = 5.) Solve: 2(3x + 4)– 3(x – 2) = 5x + 10 a. Expand using the distributive property: 2(3x + 4) = 6x + 8 and 3(x – 2) = 3x – 6 Note: Subtracting 3(x – 2) gives: –3x + 6 b. Combine like terms (apply the commutative property to reorder if needed): 6x + 8 – 3x + 6 = 3x + 14 ___________________________________ c. Write the equation: 3x + 14 = 5x + 10 d. Subtract 3x and then subtract 10: x = Mashup 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 6.) Advanced Challenge: Solve: 3[2(x + 3)– 4] + 5 = 2(3x + 8)– x a. Inside the brackets, use the distributive property: 2(x + 3) = 2x + 6; then 2x + 6 – 4 = 2x + 2 ________________________________ b. Multiply by 3 using the distributive property: 3(2x + 2) = 6x + 6; then add 5: 6x + 11 c. Expand the right side: 2(3x + 8) = 6x + 16; then subtract x: 6x + 16 – x = 5x + 16 d. Set the equation: 6x + 11 = 5x + 16 e. Subtract 5x from both sides and then subtract 11: x = Mashup 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 Answer Key 1.) a. 2(x + 3) expands to 2x + 6 → Distributive Property b. 6 + 4 = 10 → Associative/Commutative Property of Addition c. 2x + 10 = 18 → 2x = 8 → x = 4 2.) a. 5 + 3x becomes 3x + 5 → Commutative Property of Addition b. (3x + 5) + 4 = 3x + (5 + 4) = 3x + 9 → Associative Property of Addition c. 3x + 9 = x + 16 → 2x = 7 → x = 7/2 3.) a. 4(2x – 3) = 8x – 12 → Distributive Property 2(3x + 1) = 6x + 2, then 6x + 2 + 6 = 6x + 8 b. Equation: 8x – 12 = 6x + 8 c. 8x – 6x = 8 + 12 → 2x = 20 → x = 10 4.) a. Rewrite (3 – x) as (–x + 3) → Commutative Property of Addition b. Group: (2x – x) + (7 + 3) = x + 10 → Associative Property of Addition c. x + 10

FAQs

What should students do for each equation in this worksheet?

Solve the equation by showing every step and justify each step by writing the correct property from the word bank in the blanks.

Which properties are listed in the word bank?

It includes Addition Property of Equality, Subtraction Property of Equality, Division Property of Equality, Associative Property, Distributive Property, and Commutative Property.

How is the distributive property used during the problems?

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.

Sep 23, 2026

Uploaded by Bulrr