Learn to solve multistep equations.

Transcription

1 Learn to solve multistep equations.

2 Levi has half as many comic books as Jamal has. If you add 6 to the number of comic books Jamal has and then divide by 7, you get the number of comic books Brooke has. If Brooke has 30 comic books, how many comic books does Levi have? To answer this question, you need to set up an equation that requires more than two steps to solve.

3 Additional Example 1: Solving Equations That Contain Like Terms Solve 12 7b + 10b = b + 10b = b = b = 6 3b = b = 2 Combine like terms. Subtract 12 from both sides. Divide both sides by 3.

4 Solve 14 8b + 12b = b + 12b = 62 Try This: Example b = b = 48 4b = b = 12 Combine like terms. Subtract 14 from both sides. Divide both sides by 4.

5 Sometimes one side of an equation has has a variable expression as the numerator of a fraction. With this type of equation, it may help to first multiply both sides of the equation by the denominator.

6 Additional Example 2: Solving Equations That Contain Fractions Solve 3y 6 7 = 3. (7) 3y 6 7 = (7)3 Multiply both sides by 7. 3y 6 = y = 27 3y = y = 9 Add 6 to both sides. Divide both sides by 3.

7 Try This: Example 2 Solve 4y 4 8 = 14. (8) 4y 4 8 = (8)14 4y 4 = y = 116 4y = y = 29 Multiply both sides by 8. Add 4 to both sides. Divide both sides by 4.

8 Additional Example 3: Problem Solving Application Troy has three times as many trading cards as Hillary. Subtracting 9 from the number of trading cards Troy has and then dividing by 6 gives the number of cards Sean has. If Sean has 24 trading cards, how many trading cards does Hillary own?

9 Additional Example 3 Continued 1 Understand the Problem Rewrite the question as a statement. Find the number of trading cards that Hillary has. List the important information: Troy has 3 times as many trading cards as Hillary has. Subtracting 9 from the number of trading cards that Troy has and then dividing by 6 gives the number cards Sean has. Sean has 24 trading cards.

10 Additional Example 3 Continued 2 Make a Plan Let c represent the number of trading cards Hillary has. Then 3c represents the number Troy has, and 3c 9 represents the number Sean has, which 6 equals 24. Solve the equation 3c 9 = 24 for c to find the 6 number of cards Hillary has.

11 Additional Example 3 Continued 3 Solve 3c 9 6 (6) 3c 9 6 = 24 = (6)24 3c 9 = 144 3c = c = 153 3c = c = 51 Hillary has 51 cards. Multiply both sides by 6. Add 9 to both sides. Divide both sides by 3.

12 Additional Example 3 Continued 4 Look Back If Hillary has 51 cards, then Troy has 153 cards. When you subtract 9 from 153, you get 144. And 144 divided by 6 is 24, which is the number of cards that Sean has. So the answer is correct.

13 11-2 Insert Solving Lesson Multistep Title Equations Here Try This: Example 3 John is twice as old as Helen. Subtracting 4 from John s age and then dividing by 2 gives William s age. If William is 24, how old is Helen?

14 11-2 Insert Solving Lesson Multistep Title Equations Here Try This: Example 3 Continued 1 Understand the Problem Rewrite the question as a statement. Find Helen s age. List the important information: John is 2 times as old as Helen. Subtracting 4 from John s age and then dividing by 2 gives William s age. William is 24 years old.

15 11-2 Insert Solving Lesson Multistep Title Equations Here Try This: Example 3 Continued 2 Make a Plan Let h stand for Helen s age. Then 2h represents John s age, and 2h 4 represents William s age, 2 which equals 24. Solve the equation Helen s age. 2h 4 2 = 24 for h to find

16 11-2 Insert Solving Lesson Multistep Title Equations Here Try This: Example 3 Continued 3 Solve 2h 4 2 = 24 (2) 2h 4 = (2)24 Multiply both sides by h 4 = 48 2h = Add 4 to both sides. 2h = 52 2h = 52 Divide both sides by h = 26 Helen is 26 years old.

17 11-2 Insert Solving Lesson Multistep Title Equations Here Try This: Example 3 Continued 4 Look Back If Helen is 26 years old, then John is 52 years old. When you subtract 4 from 52 you get 48. And 48 divided by 2 is 24, which is the age of William. So the answer is correct.

18 11-2 Solving Insert Lesson Multistep Title Equations Here Solve. Lesson Quiz 1. c c = x x = w w = 59 c = 7 x = 4 w = k = 10 k = Kelly swam 4 times as many laps as Kathy. Adding 5 to the number of laps Kelly swam gives you the number of laps Julie swam. If Julie swam 9 laps, how many laps did Kathy swim? 1 lap

19 Homework 11-2 Worksheet Study for fraction quiz tomorrow Corrections due Friday Study for 11-1 to 11-3 quiz Friday