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Solving Two- Step Equations Lesson 4-4 Rules to Remember • When solving an equation, the goal is to get the variable by itself. 3x + 2 = 9 • Addition and Subtraction are opposites • Multiplication and Division are opposites Don’t Forget • The equation is like a balance scale. Whatever you do to one side of the equation must be done to the other side of the equation. +5 +5 How to solve two-step equations • “Undo” the operations in the reverse order of the order of operations. • Work back-words SADMEP – Add/Subtract FIRST – Multiply/Divide SECOND Let’s Try One… The problem contains addition and multiplication. Which one do we undo 1st? • 3x + 2 = 23 - 2 -2 21 3x = 21 3 3 x=7 Another Example The problem contains subtraction and multiplication. Which one do we undo 1st? • -2y – 7 = 3 +7 +7 10 -2y = 10 -2 -2 y = -5 Last Example The problem contains addition and multiplication. Which one do we undo 1st? • -3c + 9 = 3 -9 -9 -6 -3c = -6 -3 -3 c= 2 Solving Two-Step Equations Solve each equation. 18 + 3x 18 + 3x – 18 3x = 30 = 30 –18 = 12 Subtract 18 from both sides to undo the addition. 3x = 12 3 3 Divide both sides by 3 to undo the multiplication. x=4 Now it’s your turn 1. 2. 3. 4. 5. 6. 5x + 4 = 19 2t + 7 = -1 6m + 1 = -23 -4w – 4 = 8 -7y + 3 = -25 3t – 13 = 2 1. 2. 3. 4. 5. 6. x=3 t = -4 m = -4 w = -3 y=4 t=5 Solving Two-Step Equations Solve. Check the answer. x –2= 1 3 x –2= 1 3 + 2 +2 x = 3 3 3· x= 3·3 3 x=9 Add 2 to both sides to undo the subtraction. Multiply both sides by 3. Check It Out: Example 1A Solve each equation. 12 + 3x = 27 12 + 3x = 27 – 12 –12 3x = 15 Subtract 12 from both sides to undo the addition. 3x = 15 3 3 Divide both sides by 3 to undo the multiplication. x=5 Check It Out: Example 1B Solve. Check the answer. x –1= 2 2 x –1= 2 2 + 1 +1 x = 3 2 2· x= 2·3 2 x=6 Add 1 to both sides to undo the subtraction. Multiply both sides by 2.