Lesson 1 1 Objective To solve equations using

Lesson 1. 1 Objective: To solve equations using addition, subtraction, multiplication, and division Vocab: Inverse operations: Are operations that undo each other such as addition and subtraction. Isolating the Variable: means to get the variable by itself.

EX: x + 5 = – 13 subtract 5 from both sides – 5 simplify x = – 18 check – 18 + 5 = – 13 EX: – 6 = x – 9 +9 +9 3= x add 9 to both sides simplify check – 6=3– 9

EX: 7 – x = 42 – 7 subtract 7 from both sides – x = 35 +x +x we are solving for x not – x. 0 = 35 + x – 35 subtract 35 from both sides – 35 = x add x to both sides check 7 – (– 35) =42 We could of solved – x = 35 by dividing both sides by – 1

Properties of Equality Multiplication property If a = b, then ac = bc Division property If a = b, and c ≠ 0, then a ÷ c = b ÷ c EX: solve – 5 x = 30 – 5 x =– 6 Divide both sides by – 5 The -5’s cancel check – 5 • – 6 = 30

EX: x = 32 Multiply both sides by – 4 solve – 4 (– 4) x = 32 (– 4) The -4’s cancel – 4 x = – 128 check – 128 = 32 – 4 EX: solve 3 2 x Multiply each side by – — 6 = –— 3 2 3 Why – — 2 ? The reciprocal of – 2/3 is – 3/2 2 – 3 • 6 = – 3 2 – 9=x • – 3 2 x Check: - 2/3 • – 9 = 6

Practice: Solve each equation 1) – 3 x = 27 – 3 X = – 9 2) X= 40 3) X = 32