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Solving Multistep
Equations
10-2
Pre-Algebra
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
Learn to solve multistep equations.
To solve a complicated equation,
you may have to simplify the
equation first by combining like
terms.
Example: 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
Example 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 
Try This
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
Try This 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 
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.
Example: 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
Example Continued
5n + 7 = –3
– 7 –7 Subtract to undo addition.
5n
= –10
5n= –10
5
5
n = –2
Divide to undo multiplication.
Remember!
The least common denominator (LCD) is the
smallest number that each of the denominators
will divide into.
Example: 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.
Example Continued
23x – 34 = 12
Combine like terms.
+ 34 + 34
23x
= 46
23x = 46
23 23
Add to undo subtraction.
x=2
Divide to undo multiplication.
Example 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
Try This
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
Distributive Property.
Try This Continued
3n + 5 = –1
– 5 –5
3n
= –6
3n= –6
3
3
n = –2
Subtract to undo addition.
Divide to undo multiplication.
Try This
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.
Try This Continued
8x – 13 = 3
+ 13 + 13
8x
= 16
8x = 16
8
8
x=2
Combine like terms.
Add to undo subtraction.
Divide to undo multiplication.
Try This 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
Example: 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
Example 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.
Try This
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
Try This 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.
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