 # Lesson 1.1 Objective: To solve equations using addition, subtraction, multiplication, and division Are operations that undo each other such as addition.

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Lesson 1.1 Objective: To solve equations using addition, subtraction, multiplication, and division Are operations that undo each other such as addition and subtraction. Inverse operations: Isolating the Variable: Vocab: means to get the variable by itself.

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

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

– 5x = 30 Divide both sides by – 5 – 5 x = – 6 check – 5 – 6 = 30 EX: solve The -5’s cancel 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 x = 32 – 4 Multiply both sides by – 4 (– 4) x –4 = 32 The -4’s cancel x = – 128 check – 128 – 4 = 32 (– 4) EX: solve 6 = – 2 — 3 x Multiply each side by – 3 — 2 Why 3 – — 2 ? The reciprocal of –2/3 is – 3/2 – 3 2 6 = – 2 3 – 3 2 x – 9 = x Check: - 2/3 –9 = 6

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

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