Section 2.2 Day 1

A) Algebraic Properties of Equality Let a, b, and c be real numbers: 1) Addition Property – If a = b, then a + c = b + c Use them 2) Subtraction Property – If a = b, the a - c = b – c when we did 3) Multiplication Property – If a = b, the ac = bc Equation 4) Division Property – If a = b, and c ≠ 0, then a ÷ c = b ÷ c Solving. 5) Reflexive Property – For any real number a, a = a 6) Symmetric Property – If a = b, then b = a 7) Transitive Property – If a = b and b = c, then a = c 8) Substitution Property – If a = b, then a can be substituted for b in any equation or expression. 9) Distributive Property – a(b + c) = ab + ac or a(b – c) = ab - ac

Ex. 1 Solve 3x + 12 = 8x – 18 and write a reason for each step. 3x + 12 = 8x – 18 given 3x – 3x + 12 = 8x – 3x = 5x – 18 Subtraction property of equality = 5x – = 5x Addition property of equality 5 5 x = 6 Division property of equality

Student practice: Justify each step in solving the equation, in a two column proof. 1) 3x + 2 = 17 4) 2) 2(3x – 5) = 50 5) 3) 3y + 4 =