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Observation… How is problem #1 different from problem #2? 1) 214 = y + 112 How is problem #3 different from problem #4? 3) This is a one-step equation. This is a one-step equation. 2) 214 = 2y + 112 This is a two-step equation. 5x = 20 4) 5x - 25 = 20 This is a two-step equation. Solving equations in two steps Goal: 1st step: 2nd step: Tips: Solving equations in two steps Goal: get the variable (letter) by itself. 1st step: 2nd step: Tips: undo addition or subtraction undo multiplication or division Read the equation. SHOW YOUR WORK! 3x + 10 = 37 -10 -10 3x 3 x = 27 3 =9 Draw a line down the equal sign. x - 8 = 12 4 +8 +8 4 x = 20 4 4 x = 80 Cross #s out when they’re cancelled. Circle your answer. 12-1 Solving Two-Step Equations Check It Out: Example 1A Solve. Check the answer. 7c + 6 = 48 7c + 6 = 48 –6 7c –6 = 42 7c = 42 7 7 c=6 Course 2 Subtract 6 from both sides. Divide both sides by 7. 12-1 Solving Two-Step Equations Additional Example 1A: Solving Two-Step Equations Using Division Solve. Check each answer. 9c + 3 = 39 9c + 3 = 39 –3 9c –3 = 36 9c = 36 9 9 c=4 Course 2 Subtract 3 from both sides. Divide both sides by 9. 12-1 Insert TitleEquations Here SolvingLesson Two-Step Check It Out: Example 2A Solve. 8+ y 2 y 8+ 2 –8 y 2 y (2) 2 = 48 = 48 –8 = 40 Subtract 8 from both sides. = (2)40 Multiply both sides by 2. y = 80 Course 2 12-1 Insert TitleEquations Here SolvingLesson Two-Step Check It Out: Example 2B Solve. x – 31 = 19 5 x – 31 = 19 5 +31 +31 x = 50 5 x (5) 5 = (5)50 x = 250 Course 2 Add 31 to both sides. Multiply both sides by 5. 12-1 Solving Two-Step Equations Additional Example 3: Consumer Math Application Jamie rented a canoe while she was on vacation. She paid a flat rental fee of $85.00, plus $7.50 each day. Her total cost was $130.00. For how many days did she rent the canoe? Let d represent the number of days she rented the canoe. 7.5d + 85 = 130 – 85 –85 7.5d = 45 7.5d = 45 7.5 7.5 Subtract 85 from both sides. Divide both sides by 7.5. d =6 Jamie rented the canoe for 6 days. Course 2 12-1 Insert TitleEquations Here SolvingLesson Two-Step Check It Out: Example 3 Jack’s father rented a car while they were on vacation. He paid a rental fee of $20.00 per day, plus 20¢ a mile. He paid $25.00 for mileage and his total bill for renting the car was $165.00. For how many days did he rent the car? Let d represent the number of days he rented the car. 20d + 25 = 165 – 25 – 25 Subtract 25 from both sides. 20d = 140 20d = 140 Divide both sides by 20. 20 20 d =7 Jack’s father rented the car for 7 days. Course 2