1. 11-1 Solving Two-Step Equations Do Now Solve. 1. n + 9 = 17 2. 71 + z = 55 3. 6x = 42 4. n = 8 x = 7 z = -16 = 9 y = 72 y8y8

2. 11-1 Solving Two-Step Equations Learn to solve two-step equations.

3. 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.

4. 11-1 Solving Two-Step Equations A two step equation is when addition/subtraction AND multiplication/division is happening to the variable. You will need to perform two steps in order to solve the equation. GOAL: Use inverse operations to isolate the variable.

5. 11-1 Solving Two-Step Equations Steps for Solving Two-Step Equations 1.Draw “the river” 2.Get rid of any number being added or subtracted to the variable by doing the inverse operation to both sides of the equation 3.Get rid of anything being multiplied or divided to the variable by doing the inverse operation to both sides of the equation 4.Check your answer

6. 11-1 Solving Two-Step Equations Solve. Check each answer. Example A 9c + 3 = 39 – 3 –3 9c = 36 c = 4 Subtract 3 from both sides. Divide both sides by 9. 9c99c9 = 36 9

7. 11-1 Solving Two-Step Equations Check. Example A continued 9c + 3 = 39 9(4) + 3 39 ?=?= ?=?= ?=?= 36 + 3 39 39 Substitute 4 for c. 4 is a solution.

8. 11-1 Solving Two-Step Equations –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 Example A continued

9. 11-1 Solving Two-Step Equations –4m – 6 = –34 –4(7) – 6 –34 ?=?= ?=?= ?=?= –28 – 6 –34 –34 Substitute 7 for m. 7 is a solution. Check. Example A continued

10. 11-1 Solving Two-Step Equations 4. –6m – 8 = –503. 7c + 6 = 48 1. 3x + 7 = -52. 7 + 4y = 19

11. 11-1 Solving Two-Step Equations YOU TRY 1 Solve 3x + 7 = –5 3x + 7 = –5 3x = –12 x = –4 -7 -7 ANSWER The solution is –4. 3 = Dec 17

12. 11-1 Solving Two-Step Equations x = 3 –7 – 7 ANSWER The solution is 3. 7 + 4y = 19 4y = 12 4 = Solve 7 + 4y = 19 Dec 17 YOU TRY 2

13. 11-1 Solving Two-Step Equations Solve. Check the answer. 7c + 6 = 48 – 6 –6 7c = 42 c = 6 Subtract 6 from both sides. Divide both sides by 7. 7c77c7 = 42 7 YOU TRY 3

14. 11-1 Solving Two-Step Equations –6m – 8 = –50 + 8 +8 –6m = –42 Add 8 to both sides. Solve. Check the answer. m = 7 Divide both sides by –6. –6m –6 = –42 –6 YOU TRY 4

15. 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

16. 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