1. Reasoning with Properties from Algebra

2. Properties of Equality For all properties, a, b, & c are real #s. Addition property of equality- if a=b, then a+c=b+c. (can add the same #, c, to both sides of an equation) Subtraction property of equality - If a=b, then a-c=b-c. (can subtract the same #, c, from both sides of an equation) Multiplication prop. of equality- if a=b, then ac=bc. Division prop. of equality- if a=b, then

3. Properties of = (cont.) Reflexive prop. of equality- a=a Symmetric prop of equality- if a=b, then b=a. Transitive prop of equality- if a=b and b=c, then a=c. Substitution prop of equality- if a=b, then a can be plugged in for b and vice versa. Distributive prop.- a(b+c)=ab+ac OR (b+c)a=ba+ca

4. Ex: Solve the equation & write a reason for each step. 1.2(3x+1)=5x+14 2.6x+2=5x+14 3.x+2=14 4.x=12 1.Given 2.Distributive prop 3.Subtraction prop of = 4.Subtraction prop of =

5. Solve 55z-3(9z+12)=-64 & write a reason for each step. 1.55z-3(9z+12)=-64 2.55z-27z-36=-64 3.28z-36=-64 4.28z=-28 5.z=-1 1.Given 2.Distributive prop 3.Simplify (or collect like terms) 4.Addition prop of = 5.Division prop of =