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3.1 Solving 2-step equations

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3.1 – Solving 2-step Equations Goals / “I can…” Solve 2-step equations Use deductive reasoning

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3.1 – Solving 2-step Equations When looking at an algebraic equation like x + 7 = 15 we try to figure out how to get x by itself. We must get rid of the +7. To do this, we might say we undo the + 7 or do the opposite of + 7. Either way we could – 7 from both sides. x + 7 = 15 -7 -7 x = 8

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3.1 – Solving 2-step Equations When looking at an algebraic equation like ½ x = 9 we try to get x by itself. We must get rid of the multiply by ½ by doing the inverse of that which is to multiply by the reciprocal or 2. 2(½ x) = (9)2 x = 18

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To solve two-step equations, undo the operations by working backwards. Example: Ask yourself, 1.What is the first thing we are doing to x? 2.What is the second thing? Recall the order of operations as you answer these questions. Dividing by 2 Subtracting 3 To undo these steps, do the opposite operations in opposite order.

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1.Draw “the river” 2.Add 3 to both sides 3.Simplify 4.Clear the fraction -Multiply both sides by 2 5.Simplify 6.Check your answer Use a DO-UNDO chart as a shortcut to answering the questions. In the table, write the opposite operations in the opposite order DO UNDO ÷2 -3 Follow the steps in the ‘undo’ column to isolate the variable. + 3 + 3 = - 4 x = -8 -4 – 3 = -7 +3 · 2 2 · · 2

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1) Solve 2x - 1 = -3 + 1 + 1 2x = -2 2 2 x = -1 2(-1) - 1 = -3 -2 – 1 = -3 1.Draw “the river” 2.Add 1 to both sides 3.Simplify 4.Divide both sides by 2 5.Simplify 6.Check your answer D U · 2 - 1 + 1 ÷ 2

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+ 4 + 4 3 · · 3 x = 36 12 – 4 = 8 2) Solve 1.Draw “the river” 2.Add 4 to both sides 3.Simplify 4.Clear the fraction -Multiply both sides by 3 5.Simplify 6.Check your answer D U ÷ 3 - 4 + 4 · 3

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3) Solve 3y – 1 = 8 1.y = 3 2.y = -3 3.y = 4.y = Answer Now

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3) Solve d – 4 = 6 + 4 + 4 d = 10 1.Draw “the river” 2.Clear the fraction - Multiply both sides by 2 3.Simplify 4.Add 4 to both sides 5.Simplify 6.Check your answer D U - 4 ÷ 2 · 2 + 4

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4) Solve 1.d = -7 2.d = -19 3.d = -17 4.d = 17 Answer Now

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5) Solve -3 -3 a = 35 1.Draw “the river” 2.Subtract 3 from both sides 3.Simplify 4.Clear the fraction – Multiply both sides by -7 5.Simplify 6.Check your answer D U ÷ -7 + 3 - 3 · -7 Do/Undo Chart – This one is tricky! Remember to always use the sign in front of the number.

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6) Solve 5z + 16 = 51 1.z = -35 2.z = -7 3.z = 35 4.z = 7 Answer Now

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- 1 - 1 5 · · 5 3x = 15 3 3 x = 5 7) Solve 1.Draw “the river” 2.Subtract 1 from both sides 3.Simplify 4.Clear the fraction - Multiply both sides by 5 5.Simplify 6.Divide both sides by 3 7.Simplify 8.Check your answer D U · 3 ÷ 5 + 1 - 1 · 5 ÷ 3

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3.1 – Solving 2-step Equations copy A music store sells a copy of a deluxe electric guitar for $295. This is $30 more than 1/3 the cost of the deluxe electric guitar it is modeled after. What is the cost of the deluxe guitar?

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