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Activity Modeling Two-Step Equations Solving 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 x = Model the equation 2x + 3 = 7. 1 Remove three 1 -tiles from each side. 2 The coefficient of x is 2, so divide the remaining tiles on each side into 2 identical groups Keep one of these groups. One x -tile is equal to two 1 -tiles. So, the solution is 2. 4 = x x = x ++ = x x

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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? In the Real World Solving Two-Step Equations 3. 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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Divide each side by 2 to undo multiplication. Simplify. Subtract 7 from each side to undo addition. Write an algebraic model. Solving a Real-World Problem EXAMPLE 1 Solving Two-Step Equations 3. Cost to join Cost per song Number of songs Total Cost + = 7 + 2x = 23 – 7 2x = 16 2x22x = x = 8 Simplify. x is by itself. ANSWER You downloaded 8 songs. 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?

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NOTE BOOK Undo addition or subtraction. Some equations require two inverse operations to solve. Solving a Two-Step Equation Solving Two-Step Equations 3. 2x + 1 = 5 – 1 2x = 4 Simplify. 2x2x = 4 x = 2 Undo multiplication or division. Simplify. 22

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x2x2 – 14 = 8 ? Original equation Add 14 to each side to undo subtraction. Simplify. Substitute 44 for x in the original equation. Solving with a Variable in the Numerator EXAMPLE 2 –––––– + 14 –––– + 14 C HECK Solving Two-Step Equations 3. – 14 = 8 x2x2 x2x2 = 22 x2x2 2 2 Multiply each side by 2 to undo division. x = 44 Simplify – 14 = 8

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

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