11 1 Solving TwoStep Equations Do Now Solve

11 -1 Solving Two-Step Equations Do Now Solve the equation. Check you answer. 1. 9 b + 8 = 80 b = 8 2. - 8 + 2 x = -16 x = -4 3. – 10 = 20 + 6 c c = -5 4. -5 y – 3 = -18 y = 3

11 -1 Solving Two-Step Equations 1) 2) 3) 4) 5) 6) 1 3 2 2 3 4 11. 1 a homeworksheet 7) 14 13) 7 8) 9 14) 6 9) 35 15) 9 10) 5 11) 6 12) 3

11 -1 Solving Two-Step Equations Learn to solve two-step equations.

11 -1 Solving Two-Step Equations • Remember that a fraction bar means division

11 -1 Solving Two-Step Equations Example A Solve. x – 11 = 9 -7 +11 x = 20 -7 x = (-7)20 (-7) -7 x = -140 Add 11 to both sides. Multiply both sides by -7.

11 -1 Solving Two-Step Equations Example A 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

11 -1 Solving Two-Step Equations 1. 3. x – 3=1 2 x – 31 = 19 5 2. 8 + y = 48 -2 4. 3 p – 2 = -29

11 -1 Solving Two-Step Equations YOU TRY 1 Solve. x – 3=1 2 +3 +3 x =4 2 x = (2)4 (2) 2 x=8 Add 3 to both sides. Multiply both sides by 2.

11 -1 Solving Two-Step Equations YOU TRY 2 Solve. 8 + y = 48 -2 8+ – 8 y -2 = 48 – 8 y = 40 -2 y (-2)-2 = (-2)40 y = -80 Subtract 8 from both sides. Multiply both sides by -2.

11 -1 Solving Two-Step Equations YOU TRY 3 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.

11 -1 Solving Two-Step Equations YOU TRY 4 Solve. 3 p - 2 = -29 + 2 +2 3 p = -27 3 3 p = -9 Add 2 to both sides. Divide both sides by 3.

11 -1 Solving Two-Step Equations Example B 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. 5 d + 85 = 130 – 85 Subtract 85 from both sides. 7. 5 d = 45 Divide both sides by 7. 5 d = 45 7. 5 d =6 Jamie rented the canoe for 6 days.

11 -1 Solving Two-Step Equations YOU TRY 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.

11 -1 Solving Two-Step Equations Lesson Quiz Solve. Check your answers. 1. 6 x + 8 = 44 x=6 2. 14 y – 14 = 28 y=3 3. 12 = m 7 +3 v 4. – 8 – 6 = 8 z 63 = m v = – 112

11 -1 Solving Two-Step Equations Lesson Quiz 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

11 -1 Solving Two-Step Equations Lesson Quiz for Student Response Systems 6. Solve A. z = 72 B. z = 86 C. z = 90 D. z = 104

11 -1 Solving Two-Step Equations Lesson Quiz for Student Response Systems 7. 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