Transcript Lesson 2 – Solving Multistep Equations

10-2 Solving Multistep Equations
Learn to solve multistep equations.
Pre-Algebra
10-2 Solving Multistep Equations
To solve a complicated equation,
you may have to simplify the
equation first by combining like
terms.
Then solve for the variable.
Pre-Algebra
10-2 Solving Multistep Equations
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
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
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
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
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
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
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
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
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
? 2
14 + 2 – 17 =
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 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 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
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
Example 3: Money Application
When Mr. and Mrs. James left for the mall, Mrs.
James had twice as much money as Mr. James
had. While shopping, Mrs. James spent $54
and Mr. James spent $26. When they arrived
home, they had a total of $46. How much did
Mr. James have when he left home?
Let h represent the amount of money that Mr. James
had when he left home. So Mrs. James had 2h when
she left home.
h + 2h – 26 – 54 = 46
Pre-Algebra
Mr. James $+ Mrs. James $
– Mr. James spent – Mrs. James
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. James had $42 when he left home.
Pre-Algebra
10-2 Solving Multistep Equations
Try This: Example 3
When Mr. and Mrs. Keough left for the store,
Mrs. Keough had three times as much money
as Mr. Keough had. While shopping, Mr.
Keough spent $50 and Mrs. Keough spent $25.
When they arrived home, they had a total of
$25. How much did Mr. Keough have when he
left home?
Let h represent the amount of money that Mr.
Keough had when he left home. So Mrs. Keough had
3h when she left home.
Mr. Keough $ + Mrs. Keough $ –
h + 3h – 50 – 25 = 25 Mr. Keough spent – Mrs. Keough
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. Keough had $25 when he left home.
Pre-Algebra