Justifying Algebraic Equations Use the properties from the word bank to justify each step in solving the following equations.
Word Bank:
Addition Property of Equality Subtraction Property of Equality
Multiplication Property of Equality Division Property of Equality
Distributive Property Combine Like Terms
Symmetrical Property

Equation Steps Property
Given 2( − 9) = −10, Prove x = 4
1. 2( − 9) = −10 1.
2. 2 − 18 = −10 2.
3. 2 = 8 3.
4. = 4 4.
Equation Steps Property
Given 10 − 4 = 2 − 20, Prove k = – 2
1. 10 − 4 = 2 − 20 1.
2. 8 − 4 = −20 2.
3. 8 = −16 3.
4. = −2 4.
Equation Steps Property
Given 5 − 42 = 12, Prove n = – 6
1. 5 − 42 = 12 1.
2. −42 = 7 2.
3. −6 = 3.
4. = −6 4.
4.
5.
Equation Steps Property
Given −8( + 1) = −5( + 10), Prove w = 14
1. 1.
2. −8 − 8 = −5 − 50 2.
3. −3 − 8 = −50 3.
4. −3 = −42 4.
5. = 14 5.
Equation Steps Property
Given 14 − 2( + 8) = 5 − (3 − 34), Prove x = – 9
1. 1.
2. 14 − 2 − 16 = 5 − 3 + 34 2.
3. −2 − 2 = 2 + 34 3.
4. −4 − 2 = 34 4.
5. −4 = 36 5.
6. = −9