1. 2.4 Algebraic Reasoning

2. What We Will Learn
Use algebraic properties of equality to justify steps in solving
Use distributive property to justify steps in solving
Use properties of equality involving segment lengths and angle measures

3. Needed Vocab Addition Prop: If a = b, then a+c = b+c
Subtraction Prop: a-c = b-c
Multiplication prop: a⋅c = b⋅c
Division prop: 𝑎 𝑐 = 𝑏 𝑐
Substitution prop: If a = b, then a can be substituted for b (or b for a) in any equation or expression
Distributive prop: a(b+c) = ab + ac
Reflexive Prop of Equality: a = a
Symmetric Prop of Equality: If a = b, then b = a
Transitive Prop of Equality: If AB = CD and CD = EF, then AB = EF.

4. Ex. 1 Justifying Steps Start of proofs Solve and justify Statement
6x = -24
6𝑥 6 = −24 6
x = -4
Reason
Given
Addition Prop
Simplify
Division Prop

5. Your Practice Reason Given Addition Prop Simplify Division Prop
Solve and Justify
Statement
-2p – 9 = 10p – 17
+2p p
-9 = 12p – 17
8 = 12p
8 12 = 12𝑝 12
2 3 = p
Reason
Given
Addition Prop
Simplify
Division Prop

6. Ex. 2 Using Distributive Prop
Solve and Justify
-5(7w+8) = 30
-35w – 40 = 30
-35w = 70
−35𝑤 −35 = 70 −35
w = -2
Given
Distributive Prop
Addition Prop
Simplify
Division Prop

7. Ex. 3 Literal Equations Solve and Justify Solve p(r+1)=n for r
pr+p = n
-p -p
pr = n – p
𝑝𝑟 𝑝 = 𝑛−𝑝 𝑝
r = 𝑛−𝑝 𝑝
Given
Distributive prop
Subtraction prop
Simplify
Division prop

8. Your Practice Given Distributive prop Addition prop Simplify
Solve and justify
Solve s = 180(n – 2) for n
s = 180n – 360
S = 180n
𝑠 = 180𝑛 180
𝑠 =𝑛
Given
Distributive prop
Addition prop
Simplify
Division prop

9. Ex. 4 Identifying Properties
𝑚∠1=𝑚∠3
If BC = XY and XY = 8, then BC = 8
Reflexive Prop of Equality
Transitive Prop of Equality