1. 3 3 . Solving Two-Step Equations Activity Modeling Two-Step Equations
L E S S O N
3 3 .
Solving Two-Step Equations
Activity
Modeling Two-Step Equations
A two-step equation is an equation you solve using two operations. You can use algebra tiles to model and solve two-step equations.
Model and solve 2x + 3 = 7. x + + + + + + 1
Model the equation 2x + 3 = 7. = x + + + + + x 2
Remove three 1-tiles from each side. = 3
The coefficient of x is 2, so divide the remaining tiles on each side into 2 identical groups. + x = 4
Keep one of these groups. One x-tile is equal to two 1-tiles. So, the solution is 2. x + =

2. 3 3 . Solving Two-Step Equations In the Real World
L E S S O N
3 3 .
In the Real World
Music Club You pay $7 to join an Internet music club. You pay $2 for each song that you download. Your cost for joining and downloading some songs is $23. How many songs did you download?
You will answer this question in Example 1 by solving the two-step equation 7 + 2x = 23. The value of x is the number of songs you downloaded.

3. 3 3 . 1 Solving Two-Step Equations – 7 – 7
L E S S O N
3 3 .
EXAMPLE 1
Solving a Real-World Problem
You pay $7 to join an Internet music club. You pay $2 for each song that you download. Your cost for joining and downloading some songs is $23. How many songs did you download?
Cost
to join
per song
Number
of songs
Total +  =
7 + 2x = 23
Write an algebraic model.
– 7
– 7
Subtract 7 from each side to undo addition.
2x = 16
Simplify. 2x 2 16 2 =
Divide each side by 2 to undo multiplication.
x = 8
Simplify. x is by itself.
ANSWER
You downloaded 8 songs.

4. Solving a Two-Step Equation
Solving Two-Step Equations
L E S S O N
3 3 .
NOTE
BOOK
Solving a Two-Step Equation
Some equations require two inverse operations to solve.
2x + 1 = 5
2x = 5
– 1
– 1
Undo addition or subtraction.
2x = 4
Simplify. 2x = 4
Undo multiplication or division. 2 2
x = 2
Simplify.

5. 3 3 . 2 Solving Two-Step Equations + 14
L E S S O N
3 3 .
EXAMPLE 2
Solving with a Variable in the Numerator
– 14 = 8 x 2
Original equation
––––––
+ 14
––––
+ 14
Add 14 to each side to undo subtraction. x 2
= 22
Simplify. x 2
= 22
• 2
Multiply each side by 2 to undo division.
x = 44
Simplify.
CHECK x 2
– 14 = 8 ? 44
Substitute 44 for x in the original equation.
22 – 14 = 8

6. 3 3 . 3 Solving Two-Step Equations – 12
L E S S O N
3 3 .
EXAMPLE 3
Solving with a Negative Coefficient
8 = 12 – 2x
Original equation
= 12 – 2x
– 12
Subtract 12 from each side to undo addition.
–4 = –2x
Simplify.
–2x –4 =
Divide each side by –2 to undo multiplication. –2
2 = x
Simplify.