Transcript 10-2

10-2
10-2Solving
SolvingMultistep
MultistepEquations
Equations
Homework & Learning Goal
Lesson Presentation
6th Grade AIMS Prep
Pre-Algebra
Pre-Algebra
10-2 Solving Multistep Equations
PA HOMEWORK ANSWERS
Page 500
#8-30 EVENS
Pre-Algebra
10-2 Solving Multistep Equations
Pre-Algebra HOMEWORK
Page 504
#12-30 EVENS
Pre-Algebra
10-2 Solving Multistep Equations
Our Learning Goal
Students will be able to solve
multi-step equations with
multiple variables, solve
inequalities and graph the
solutions on a number line.
Pre-Algebra
10-2 Solving Multistep Equations
Our Learning Goal Assignments
• Learn to solve two-step equations.
• Learn to solve multistep equations.
• Learn to solve equations with variables on both
sides of the equal sign.
• Learn to solve two-step inequalities and graph
the solutions of an inequality on a number line.
• Learn to solve an equation for a variable.
• Learn to solve systems of equations.
Pre-Algebra
10-2 Solving Multistep Equations
Today’s Learning Goal Assignment
Learn to solve
multistep
equations.
Pre-Algebra
10-2 Solving Multistep Equations
REMEMBER!!
To solve a complicated
equation, you may have
to simplify the equation
first by combining like
terms.
Pre-Algebra
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
Pre-Algebra
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 
Pre-Algebra
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
Pre-Algebra
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 
Pre-Algebra
10-2 Solving Multistep Equations
ANOTHER THANG to REMEMBER
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.
Pre-Algebra
10-2 Solving Multistep Equations
O’Wait, another thingy to Remember!
The least common
denominator (LCD) is the
smallest number that each
of the denominators will
divide into.
Pre-Algebra
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
Pre-Algebra
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
Pre-Algebra
Divide to undo multiplication.
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
Pre-Algebra
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
Pre-Algebra
Subtract to undo addition.
Divide to undo multiplication.
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.
Pre-Algebra
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
Pre-Algebra
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
Pre-Algebra
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.
Pre-Algebra
10-2 Solving Multistep Equations
Try This: Example 2B Continued
8x – 13 = 3
+ 13 + 13
8x
= 16
8x = 16
8
8
x=2
Pre-Algebra
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
Pre-Algebra
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
Pre-Algebra
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.
Pre-Algebra
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
Pre-Algebra
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.
Pre-Algebra
10-2 Solving Multistep Equations
Don’t forget your proper heading! Trade & Grade!
10-2 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
Pre-Algebra
th
6
Grade AIMS Prep
Recall some test-taking tricks that you
use to “win” on the AIMS Math.
Use at least one to solve the following
example!
AIMS Example 2