13 3 . Solving Two-Step Equations Activity Modeling Two-Step Equations L E S S O N3 3.Solving Two-Step EquationsActivityModeling Two-Step EquationsA 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++++++1Model the equation 2x + 3 = 7.=x+++++x2Remove three 1-tiles from each side.=3The coefficient of x is 2, so divide the remaining tiles on each side into 2 identical groups.+x=4Keep one of these groups. One x-tile is equal to two 1-tiles. So, the solution is 2.x+=
23 3 . Solving Two-Step Equations In the Real World L E S S O N3 3.In the Real WorldMusic 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.
33 3 . 1 Solving Two-Step Equations – 7 – 7 L E S S O N3 3.EXAMPLE1Solving a Real-World ProblemYou 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?Costto joinper songNumberof songsTotal+=7 + 2x = 23Write an algebraic model.– 7– 7Subtract 7 from each side to undo addition.2x = 16Simplify.2x2162=Divide each side by 2 to undo multiplication.x = 8Simplify. x is by itself.ANSWERYou downloaded 8 songs.
4Solving a Two-Step Equation Solving Two-Step EquationsL E S S O N3 3.NOTEBOOKSolving a Two-Step EquationSome equations require two inverse operations to solve.2x + 1 = 52x = 5– 1– 1Undo addition or subtraction.2x = 4Simplify.2x=4Undo multiplication or division.22x = 2Simplify.
53 3 . 2 Solving Two-Step Equations + 14 L E S S O N3 3.EXAMPLE2Solving with a Variable in the Numerator– 14 = 8x2Original equation––––––+ 14––––+ 14Add 14 to each side to undo subtraction.x2= 22Simplify.x2= 22• 2Multiply each side by 2 to undo division.x = 44Simplify.CHECKx2– 14 = 8?44Substitute 44 for x in the original equation.22 – 14 = 8
63 3 . 3 Solving Two-Step Equations – 12 L E S S O N3 3.EXAMPLE3Solving with a Negative Coefficient8 = 12 – 2xOriginal equation= 12 – 2x– 12Subtract 12 from each side to undo addition.–4 = –2xSimplify.–2x–4=Divide each side by –2 to undo multiplication.–22 = xSimplify.