2 6 Solving TwoStep Equations Warm Up Problem

2 -6 Solving Two-Step Equations Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

2 -6 Solving Two-Step Equations Warm Up Solve. 1. n + 9 = 17 n=8 2. 6 x = 42 x=7 3. 71 – z = 55 z = 16 y 4. 8= 9 y = 72

2 -6 Solving Two-Step Equations Problem of the Day Rhombus ABCD has a perimeter of 19 cm. If you subtract 1. 88 from the length of side BC and then divide the result by 7, you get 0. 41. What is the length of side BC? 19 ÷ 4 = 4. 75 cm (All sides of a rhombus are the same length. )

2 -6 Solving Two-Step Equations Sunshine State Standards MA. 7. A. 3. 3 Formulate and use different strategies to solve…two-step…linear equations. Also MA. 7. A. 3. 4

2 -6 Solving Two-Step Equations When you solve equations that have one operation, you use an inverse operation to isolate the variable. n + 7 = 15 – 7 n = 8 You can also use inverse operations to solve equations that have more than one operation. 2 x + 3 = 23 – 3 2 x = 20 Use the inverse of mulitplication to isolate x.

2 -6 Solving Two-Step Equations Additional Example 1 A: Solving Two-Step Equations Using Division Solve. Check each answer. 9 c + 3 = 39 – 3 9 c = 36 9 9 c=4 Subtract 3 from both sides. Divide both sides by 9.

2 -6 Solving Two-Step Equations Additional Example 1 A Continued Check. 9 c + 3 = 39 ? 39 9(4) + 3 = Substitute 4 for c. ? 39 36 + 3 = ? 39 39 = 4 is a solution.

2 -6 Solving Two-Step Equations Helpful Hint Reverse the order of operations when solving equations that have more than one operation.

2 -6 Solving Two-Step Equations Additional Example 1 B: Solving Two-Step Equations Using Division Solve. Check the answer. – 34 = – 4 m – 6 +6 +6 – 28 = – 4 m – 4 7=m Add 6 to both sides. Divide both sides by – 4.

2 -6 Solving Two-Step Equations Additional Example 1 B Continued Check. – 4 m – 6 = – 34 ? – 34 – 4(7) – 6 = Substitute 7 for m. ? – 34 – 28 – 6 = ? – 34 = – 34 7 is a solution.

2 -6 Solving Two-Step Equations Check It Out: Example 1 A Solve. Check the answer. 7 c + 6 = 48 – 6 7 c = 42 7 7 c=6 Subtract 6 from both sides. Divide both sides by 7.

2 -6 Solving Two-Step Equations Check It Out: Example 1 A Continued Check. 7 c + 6 = 48 ? 48 7(6) + 6 = Substitute 6 for c. ? 48 42 + 6 = ? 48 48 = 6 is a solution.

2 -6 Solving Two-Step Equations Check It Out: Example 1 B Solve. Check the answer. – 6 m – 8 = – 50 +8 +8 – 6 m = – 42 – 6 m=7 Add 8 to both sides. Divide both sides by – 6.

2 -6 Solving Two-Step Equations Check It Out: Example 1 B Continued Check. – 6 m – 8 = – 50 ? – 50 – 6(7) – 8 = Substitute 7 for m. ? – 50 – 42 – 8 = ? – 50 = – 50 7 is a solution.

2 -6 Solving Two-Step Equations Additional Example 2 A: Solving Two-Step Equations Using Multiplication Solve. 6 + y = 21 5 6+ – 6 (5) y 5 y 5 = 21 – 6 = 15 Subtract 6 from both sides. = (5)15 Multiply both sides by 5. y = 75

2 -6 Solving Two-Step Equations Additional Example 2 B: Solving Two-Step Equations Using Multiplication Solve. 5=z – 7 6 z 5= – 7 6 +7 +7 12 = z 6 (6)12 = z (6) 6 72 = z Add 7 to both sides. Multiply both sides by 6.

2 -6 Solving Two-Step Equations Check It Out: Example 2 A Solve. 8 + y = 48 2 8+ – 8 (2) y 2 = 48 – 8 y = 40 2 Subtract 8 from both sides. y 2 Multiply both sides by 2. = (2)40 y = 80

2 -6 Solving Two-Step Equations Check It Out: Example 2 B Solve. x – 31 = 19 5 +31 x = 50 5 x = (5)50 (5) 5 x = 250 Add 31 to both sides. Multiply both sides by 5.

2 -6 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. 00 each day. Her total cost was $127. 00. For how many days did she rent the canoe? Let d represent the number of days she rented the canoe. 7 d + 85 = 127 – 85 Subtract 85 from both sides. 7 d = 42 Divide both sides by 7. 7 d = 42 7 7 d =6 Jamie rented the canoe for 6 days.

2 -6 Solving Two-Step Equations 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. 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. 20 d + 25 = 165 – 25 Subtract 25 from both sides. 20 d = 140 Divide both sides by 20. 20 20 d =7 Jack’s father rented the car for 7 days.

2 -6 Solving Two-Step Equations Lesson Quizzes Standard Lesson Quiz for Student Response Systems

2 -6 Solving Two-Step Equations Lesson Quiz Solve. Check your answers. 1. 6 x + 8 = 44 x=6 2. 14 y – 14 = 28 y = 3 m 3. 12 = 7 + 3 4. v – 8 – 6=8 63 = m v = – 112 5. Last Sunday, the Humane Society had a 3 -hour adoption clinic. During the week the clinic is open for 2 hours on days when volunteers are available. If the Humane Society was open for a total of 9 hours last week, how many weekdays was the clinic open? 3 days

2 -6 Solving Two-Step Equations Lesson Quiz for Student Response Systems 1. Solve 7 q + 5 = 68. A. q = 6 B. q = 7 C. q = 8 D. q = 9

2 -6 Solving Two-Step Equations Lesson Quiz for Student Response Systems 2. Solve 17 h – 10 = 75. A. h = 5 B. h = 7 C. h = 9 D. h = 10

2 -6 Solving Two-Step Equations Lesson Quiz for Student Response Systems 3. Solve A. z = 72 B. z = 86 C. z = 90 D. z = 104

2 -6 Solving Two-Step Equations Lesson Quiz for Student Response Systems 4. A taxi charges an airport pickup fee of $3 plus $1. 50 for each mile traveled. If a taxi ride cost John $36, how many miles did John travel in the taxi? A. 21 miles B. 22 miles C. 31 miles D. 32 miles