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**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 + =

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**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.

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**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.

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**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.

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**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

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**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.

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Solve an equation using subtraction EXAMPLE 1 Solve x + 7 = 4. x + 7 = 4x + 7 = 4 Write original equation. x + 7 – 7 = 4 – 7 Use subtraction property of.

Solve an equation using subtraction EXAMPLE 1 Solve x + 7 = 4. x + 7 = 4x + 7 = 4 Write original equation. x + 7 – 7 = 4 – 7 Use subtraction property of.

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