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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 – 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 –7 – x = 35 +x +x 0 = 35 + x – 35 –35 – 35 = x subtract 7 from both sides we are solving for x not – x. add x to both sides subtract 35 from 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 – 5x = 30 –5 –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) –3x = 27 –3 2) –3 x 10 4 x 4 10 4 4 3) X = –9 X= 40 1 x 8 4 4 1 4 x 8 1 4 1 X = 32