Geometry, Chapter 2, Algebraic Properties

Distributive Property

3(p - 7) = 3p - 21

Reasons: 1. Given 2. Distributive Property 3. Subtraction Property 4. Division Property

Given: -8(x-3) = -32 Prove: x=7

Reasons: 1. Given 2. Distributive Property 3. Simplify/Combine like terms 4. Subtraction Property 5. Addition Property 6. Division Property

Given: 18x - 2(3x+1) = 5x - 16 Prove: x=-2

Reasons: 1. Given 2. Distributive Property 3. Addition Property 4. Division Property

Given: 2(x-9) = -10 Prove: x = 4

Reasons: 1. Given 2. Distributive Property 3. Addition Property 4. Subtraction Property 5. Division Property

Given: 2x + 30 = -4(5x - 2) Prove: x= -1

Reasons: 1. Given 2. Addition Property 3. Division Property

Given: 4x - 1 = 27 Prove: x = 7

Reasons 1. Given 2. Subtraction Property 3. Division Property 4. Symmetric Property

Given: 5n -42 =12n Prove n= -6

Reasons: 1. Given 2. Subtraction Property 3. Addition Property 4. Division Property 5. Symmetric Property

Given: 6x + 7 = 8x -17 Prove: x = 12

Division Property

If -7k = -42, then k = 6

Subtraction Property of Equality

If a = 2b, then a - c = 2b - c

Addition Property of Equality

If c - 9 = -1, then c = 8

Substitution Property

If m + n = 15 and n = 2, then m + 2 = 15

Symmetric Property

If n = -3, then -3 = n

Multiplication Property

If x/4 = 5, x= -20

Reflexive Property

x = x