1. 11-1 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 –7 n = 8 2x + 3 = 23 – 3 2x = 20 You need to use another operation to isolate x. You can also use inverse operations to solve equations that have more than one operation.

2. 11-1 Solving Two-Step Equations Solve. Check each answer. Additional Example 1A: Solving Two-Step Equations Using Division 9c + 3 = 39 – 3 –3 9c = 36 c = 4 Subtract 3 from both sides. Divide both sides by 9. 9c99c9 = 36 9

3. 11-1 Solving Two-Step Equations Check. Additional Example 1A Continued 9c + 3 = 39 9(4) + 3 39 ?=?= ?=?= ?=?= 36 + 3 39 39 Substitute 4 for c. 4 is a solution.

4. 11-1 Solving Two-Step Equations Reverse the order of operations when solving equations that have more than one operation. Helpful Hint

5. 11-1 Solving Two-Step Equations Additional Example 1B: Solving Two-Step Equations Using Division –34 = –4m – 6 + 6 +6 –28 = –4m Add 6 to both sides. Solve. Check the answer. 7 = m Divide both sides by –4. –28 –4 = –4m –4

6. 11-1 Solving Two-Step Equations Additional Example 1B Continued –4m – 6 = –34 –4(7) – 6 –34 ?=?= ?=?= ?=?= –28 – 6 –34 –34 Substitute 7 for m. 7 is a solution. Check.

7. 11-1 Solving Two-Step Equations Solve. Additional Example 2A: Solving Two-Step Equations Using Multiplication 6 + y5y5 = 21 y5y5 6 + – 6 –6 y5y5 = 15 y5y5 = (5)15(5) ‏ y = 75 Subtract 6 from both sides. Multiply both sides by 5.

8. 11-1 Solving Two-Step Equations Solve. Additional Example 2B: Solving Two-Step Equations Using Multiplication x7x7 – 11 = 9 x7x7 x7x7 = 20 x7x7 = (7)20 (7) ‏ x = 140 Add 11 to both sides. Multiply both sides by 7. +11 +11

9. 11-1 Solving Two-Step Equations Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems

10. 11-1 Solving Two-Step Equations Lesson Quiz Solve. Check your answers. 1. 6x + 8 = 44 2. 14y – 14 = 28 3. 4. y = 3 x = 6 63 = m v = –112 m7m7 12 = + 3 – 6 = 8 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 v –8

11. 11-1 Solving Two-Step Equations 1. Solve 7q + 5 = 68. A. q = 6 B. q = 7 C. q = 8 D. q = 9 Lesson Quiz for Student Response Systems

12. 11-1 Solving Two-Step Equations 2. Solve 17h – 10 = 75. A. h = 5 B. h = 7 C. h = 9 D. h = 10 Lesson Quiz for Student Response Systems

13. 11-1 Solving Two-Step Equations 3. Solve A. z = 72 B. z = 86 C. z = 90 D. z = 104 Lesson Quiz for Student Response Systems

14. 11-1 Solving Two-Step Equations 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 Lesson Quiz for Student Response Systems