Transcript Multistep Equations - Caldwell County Schools

10-2 Solving Multistep Equations
Warm Up
Problem of the Day
Lesson Presentation
Course 3
10-2 Solving Multistep Equations
Warm Up
Solve.
1. 3x = 102
x = 34
2. y = 15 y = 225
15
3. z – 100 = –1 z = 99
4. 1.1 + 5w = 98.6 w = 19.5
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
Course 3
10-2 Solving Multistep Equations
Learn to solve 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.
Course 3
10-2 Solving Multistep Equations
Additional Example 1: Solving Equations That
Contain Like Terms
Solve.
8x + 6 + 3x – 2 = 37
11x + 4 = 37 Combine like terms.
– 4 – 4 Subtract to undo addition.
11x
= 33
11x = 33 Divide to undo multiplication.
11 11
x=3
Course 3
10-2 Solving Multistep Equations
Additional Example 1 Continued
Check
8x + 6 + 3x – 2 = 37
?
8(3) + 6 + 3(3) – 2 = 37
Substitute 3 for x.
?
24 + 6 + 9 – 2 = 37
?
37 = 37 
Course 3
10-2 Solving Multistep Equations
Try This: Example 1
Solve.
9x + 5 + 4x – 2 = 42
13x + 3 = 42 Combine like terms.
– 3 – 3 Subtract to undo addition.
13x
= 39
13x = 39 Divide to undo multiplication.
13 13
x=3
Course 3
10-2 Solving Multistep Equations
Try This: Example 1 Continued
Check
9x + 5 + 4x – 2 = 42
?
9(3) + 5 + 4(3) – 2 = 42
Substitute 3 for x.
?
27 + 5 + 12 – 2 = 42
?
42 = 42 
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.
Course 3
10-2 Solving Multistep Equations
Additional Example 2: Solving Equations That
Contain Fractions
Solve.
A. 5n+ 7 = – 3
4
4
4
Multiply both sides by 4 to clear fractions,
and then solve.
4 5n + 7 = 4 –3
4
4
4
(
) ( )
7 = 4 –3 Distributive Property.
4(5n
+
4
(4 ) (4)
4)
5n + 7 = –3
Course 3
10-2 Solving Multistep Equations
Additional Example 2 Continued
5n + 7 = –3
– 7 –7 Subtract to undo addition.
5n
= –10
5n= –10
5
5
n = –2
Course 3
Divide to undo multiplication.
10-2 Insert
Title
Here
SolvingLesson
Multistep
Equations
Remember!
The least common denominator (LCD) is the
smallest number that each of the denominators
will divide into.
Course 3
10-2 Solving Multistep Equations
Additional Example 2B: Solving Equations That
Contain Fractions
Solve.
B. 7x + x – 17 = 2
3
2
9
9
The LCD is 18.
Multiply both
17
7x
x
2
18
+ –
= 18
sides by the LCD.
9
2 9
3
7x
x
17
2 Distributive
18 9 + 18 2 – 18 9 = 18 3 Property.
()
(
()
)
()
()
14x + 9x – 34 = 12
23x – 34 = 12 Combine like terms.
Course 3
10-2 Solving Multistep Equations
Additional Example 2B Continued
23x – 34 = 12
Combine like terms.
+ 34 + 34
23x
= 46
23x = 46
23 23
Add to undo subtraction.
x=2
Course 3
Divide to undo multiplication.
10-2 Solving Multistep Equations
Additional Example 2B Continued
Check
7x + x – 17 = 2
2
3
9
9
? 2
7(2) + (2) – 17 =
Substitute 2 for x.
9
2
9
3
14 2 17 ? 2
9 +2 – 9 =3
? 2
14 + 1 – 17 =
9
9
3
14 9 17 ? 6
The LCD is 9.
9 +9 – 9 =9
? 6
6=
9 9
Course 3
10-2 Solving Multistep Equations
Try This: Example 2A
Solve.
A. 3n+ 5 = – 1
4
4
4
Multiply both sides by 4 to clear fractions,
and then solve.
4 3n + 5 = 4 –1
4
4
4
(
) ( )
5 = 4 –1
4(3n
+
4
(4 ) (4)
4)
3n + 5 = –1
Course 3
Distributive Property.
10-2 Solving Multistep Equations
Try This: Example 2A Continued
3n + 5 = –1
– 5 –5
3n
= –6
3n= –6
3
3
n = –2
Course 3
Subtract to undo addition.
Divide to undo multiplication.
10-2 Solving Multistep Equations
Try This: Example 2B
Solve.
B. 5x + x – 13 = 1
3
3
9
9
The LCD is 9.
1
13
5x
x
9
+ –
=9 3
9
3 9
5x
x
13
1
9 9 +9 3 –9 9 =9 3
(
) ()
() () () ()
Multiply both
sides by the LCD.
Distributive
Property.
5x + 3x – 13 = 3
8x – 13 = 3 Combine like terms.
Course 3
10-2 Solving Multistep Equations
Try This: Example 2B Continued
8x – 13 = 3
+ 13 + 13
8x
= 16
8x = 16
8
8
x=2
Course 3
Combine like terms.
Add to undo subtraction.
Divide to undo multiplication.
10-2 Solving Multistep Equations
Try This: Example 2B Continued
Check
5x + x – 13 = 1
3
3
9
9
? 1
5(2) + (2) – 13 =
Substitute 2 for x.
9
3
9
3
10 2 13 ? 1
9 +3 – 9 =3
? 3
10 + 6 – 13 =
The LCD is 9.
9
9
9
9
? 3
3=
9 9
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
Course 3
Mr. Harris $+ Mrs. Harris $
– Mr. Harris spent – Mrs.
Harris spent = amount left
10-2 Solving Multistep Equations
Additional Example 3 Continued
3h – 80 = 46
+ 80 +80
3h
= 126
3h 126
3= 3
h = 42
Combine like terms.
Add 80 to both sides.
Divide both sides by 3.
Mr. Harris had $42 when he left home.
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.
Mr. Wesner $ + Mrs. Wesner $
h + 3h – 50 – 25 = 25 – Mr. Wesner spent – Mrs.
Wesner spent = amount left
Course 3
10-2 Solving Multistep Equations
Try This: Example 3 Continued
4h – 75 = 25
+ 75 +75
4h
= 100
4h 100
4= 4
h = 25
Combine like terms.
Add 75 to both sides.
Divide both sides by 4.
Mr. Wesner had $25 when he left home.
Course 3
10-2 Solving
Insert Lesson
Multistep
Title
Equations
Here
Lesson Quiz
Solve.
1. 6x + 3x – x + 9 = 33 x = 3
2. –9 = 5x + 21 + 3x
3. 5 + x = 33
8
8
8
4. 6x – 2x = 25
7
21
21
x = –3.75
x = 28
9
x = 116
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? $8.50
Course 3