1. Solving Multistep Equations
10-2
Solving Multistep Equations
Course 3
Warm Up
Problem of the Day
Lesson Presentation

2. Solving Multistep Equations
Course 3
10-2
Solving Multistep Equations
Warm Up
Solve.
1. 3x = 102
= 15
3. z – 100 = –1
w = 98.6
x = 34 y 15
y = 225
z = 99
w = 19.5

3. Solving Multistep Equations
Course 3
10-2
Solving Multistep Equations
Problem of the Day
Ana has twice as much money as Ben, and Ben has three times as much as Clio. Together they have $160. How much does each person have?
Ana, $96; Ben, $48; Clio, $16

4. Solving Multistep Equations
Course 3
10-2
Solving Multistep Equations
Learn to solve multistep equations.

5. Solving Multistep Equations
Course 3
10-2
Solving Multistep Equations
To solve a complicated equation, you may have to simplify the equation first by combining like terms.

6. Additional Example 1: Solving Equations That Contain Like Terms
Course 3
10-2
Solving Multistep Equations
Additional Example 1: Solving Equations That Contain Like Terms
Solve.
8x x – 2 = 37
11x + 4 = 37 Combine like terms.
– 4 – 4 Subtract to undo addition.
11x = 33 33 11
11x =
Divide to undo multiplication.
x = 3

7. Additional Example 1 Continued
Course 3
10-2
Solving Multistep Equations
Additional Example 1 Continued
Check
8x x – 2 = 37
8(3) (3) – 2 = 37 ?
Substitute 3 for x.
– 2 = 37 ?
37 = 37 ? 

8. Solving Multistep Equations
Course 3
10-2
Solving Multistep Equations
Try This: Example 1
Solve.
9x x – 2 = 42
13x + 3 = 42 Combine like terms.
– 3 – 3 Subtract to undo addition.
13x = 39 39 13
13x =
Divide to undo multiplication.
x = 3

9. Try This: Example 1 Continued
Course 3
10-2
Solving Multistep Equations
Try This: Example 1 Continued
Check
9x x – 2 = 42
9(3) (3) – 2 = 42 ?
Substitute 3 for x.
– 2 = 42 ?
42 = 42 ? 

10. Solving Multistep Equations
Course 3
10-2
Solving Multistep Equations
If an equation contains fractions, it may help to multiply both sides of the equation by the least common denominator (LCD) to clear the fractions before you isolate the variable.

11. Additional Example 2: Solving Equations That Contain Fractions
Course 3
10-2
Solving Multistep Equations
Additional Example 2: Solving Equations That Contain Fractions
Solve.
A = – 5n 4 7 4 3 4
Multiply both sides by 4 to clear fractions, and then solve.
( ) ( ) 7 4 –3 5n
= 4
( ) ( ) ( ) 5n 4 7 –3
= 4
Distributive Property.
5n + 7 = –3

12. Additional Example 2 Continued
Course 3
10-2
Solving Multistep Equations
Additional Example 2 Continued
5n + 7 = –3
– 7 –7 Subtract to undo addition.
5n = –10 5n 5
–10 =
Divide to undo multiplication.
n = –2

13. Insert Lesson Title Here
Course 3
10-2
Solving Multistep Equations
Insert Lesson Title Here
The least common denominator (LCD) is the smallest number that each of the denominators will divide into.
Remember!

14. Additional Example 2B: Solving Equations That Contain Fractions
Course 3
10-2
Solving Multistep Equations
Additional Example 2B: Solving Equations That Contain Fractions
Solve.
B – = x 2 7x 9 17 2 3
The LCD is 18.
( ) x 2 3 7x 9 17
– = 18
Multiply both sides by the LCD.
18( ) + 18( ) – 18( ) = 18( ) 7x 9 x 2 17 3
Distributive Property.
14x + 9x – 34 = 12
23x – 34 = 12 Combine like terms.

15. Additional Example 2B Continued
Course 3
10-2
Solving Multistep Equations
Additional Example 2B Continued
23x – 34 = Combine like terms.
Add to undo subtraction.
23x = 46 =
23x 23 46
Divide to undo multiplication.
x = 2

16. Additional Example 2B Continued
Course 3
10-2
Solving Multistep Equations
Additional Example 2B Continued
Check x 2 7x 9 17 2 3
+ – = 2 3
Substitute 2 for x.
7(2) 9
– =
(2) 17 ? 2 3 14 9
+ – = 17 ? 2 3 14 9
+ – = 17 ? 1
The LCD is 9. 6 9 14
+ – = 17 ? 6 9 = ? 

17. Solving Multistep Equations
Course 3
10-2
Solving Multistep Equations
Try This: Example 2A
Solve.
A = – 3n 4 5 4 1 4
Multiply both sides by 4 to clear fractions, and then solve.
( ) ( ) 5 4 –1 3n
= 4
( ) ( ) ( ) 3n 4 5 –1
= 4
Distributive Property.
3n + 5 = –1

18. Try This: Example 2A Continued
Course 3
10-2
Solving Multistep Equations
Try This: Example 2A Continued
3n + 5 = –1
– 5 – Subtract to undo addition.
3n = –6 3n 3 –6 =
Divide to undo multiplication.
n = –2

19. Solving Multistep Equations
Course 3
10-2
Solving Multistep Equations
Try This: Example 2B
Solve.
B – = x 3 5x 9 13 1 3
The LCD is 9.
( ) x 3 1 5x 9 13
– = 9( )
Multiply both sides by the LCD.
9( ) + 9( )– 9( ) = 9( ) 5x 9 x 3 13 1
Distributive Property.
5x + 3x – 13 = 3
8x – 13 = 3 Combine like terms.

20. Try This: Example 2B Continued
Course 3
10-2
Solving Multistep Equations
Try This: Example 2B Continued
8x – 13 = Combine like terms.
Add to undo subtraction.
8x = 16 = 8x 8 16
Divide to undo multiplication.
x = 2

21. Try This: Example 2B Continued
Course 3
10-2
Solving Multistep Equations
Try This: Example 2B Continued
Check x 3 5x 9 13 1 3
+ – = 1 3
Substitute 2 for x.
5(2) 9
– =
(2) 13 ? 1 3 10 9
+ – = 2 13 ?
The LCD is 9. 3 9 10
+ – = 6 13 ? 3 9 = ? 

22. Additional Example 3: Money Application
Course 3
10-2
Solving Multistep Equations
Additional Example 3: Money Application
When Mr. and Mrs. Harris left for the mall, Mrs. Harris had twice as much money as Mr. Harris had. While shopping, Mrs. Harris spent $54 and Mr. Harris spent $26. When they arrived home, they had a total of $46. How much did Mr. Harris have when he left home?
Let h represent the amount of money that Mr. Harris had when he left home. So Mrs. Harris had 2h when she left home.
h + 2h – 26 – 54 = 46
Mr. Harris $+ Mrs. Harris $ – Mr. Harris spent – Mrs. Harris spent = amount left

23. Additional Example 3 Continued
Course 3
10-2
Solving Multistep Equations
Additional Example 3 Continued
3h – 80 = 46
Combine like terms.
Add 80 to both sides.
3h = 126 3h 3
126 =
Divide both sides by 3.
h = 42
Mr. Harris had $42 when he left home.

24. Solving Multistep Equations
Course 3
10-2
Solving Multistep Equations
Try This: Example 3
When Mr. and Mrs. Wesner left for the store, Mrs. Wesner had three times as much money as Mr. Wesner had. While shopping, Mr. Wesner spent $50 and Mrs. Wesner spent $25. When they arrived home, they had a total of $25. How much did Mr. Wesner have when he left home?
Let h represent the amount of money that Mr. Wesner had when he left home. So Mrs. Wesner had 3h when she left home.
h + 3h – 50 – 25 = 25
Mr. Wesner $ + Mrs. Wesner $ – Mr. Wesner spent – Mrs. Wesner spent = amount left

25. Try This: Example 3 Continued
Course 3
10-2
Solving Multistep Equations
Try This: Example 3 Continued
4h – 75 = 25
Combine like terms.
Add 75 to both sides.
4h = 100 4h 4
100 =
Divide both sides by 4.
h = 25
Mr. Wesner had $25 when he left home.

26. Solving Multistep Equations Insert Lesson Title Here
Course 3
10-2
Solving Multistep Equations
Insert Lesson Title Here
Lesson Quiz
Solve.
1. 6x + 3x – x + 9 = 33
2. –9 = 5x x =
5. Linda is paid double her normal hourly rate for each hour she works over 40 hours in a week. Last week she worked 52 hours and earned $544. What is her hourly rate?
x = 3
x = –3.75 5 8 x 8 33 8
x = 28
x = 1 9 16
– = 6x 7 2x 21 25 21
$8.50