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Explore 2-3: Algebra Lab Solving Multi-Step Equations Use algebra tiles to solve each equation. 1. 3x – 7 = –10 SOLUTION: the mat. Place 10 negative 1-tiles on the other side. Remove 7 negative 1-tiles from each side. Separate the remaining tiles into 3 equal groups to match the 3 x-tiles. Each x-tile is paired with 1 negative 1-tiles. The resulting equation is x = –1. 2. 2x + 5 = 9 SOLUTION: 1 1 2 2 3 4 3 4 Place 3 x-tiles and 7 negative 1-tiles on one side of the mat. Place 10 negative 1-tiles on the other side. Remove 7 negative 1-tiles from each side. Separate the remaining tiles into 3 equal groups to match the 3 x-tiles. Each x-tile is paired with 1 negative 1-tiles. The resulting equation is x = –1. 2. 2x + 5 = 9 SOLUTION: Place 2 x-tiles and 5 positive 1-tiles on one side of the mat. Place 9 positive 1-tiles on the other side. Remove 5 positive 1-tiles from each side. Separate the remaining tiles into 2 equal groups to match the 2 x-tiles. Each x-tile is paired with 2 positive 1-tiles. The resulting equation is x = 2. 3. 5x – 7 = 8 SOLUTION: 1 1 2 eSolutions 2 Manual - Powered by Cognero Page 1 the mat. Place 9 positive 1-tiles on the other side. Remove 5 positive 1-tiles from each side. Separate the remaining tiles into 2 equal groups to match the 2 x-tiles. Each x-tile isLab paired with Multi-Step Equations Explore 2-3: Algebra Solving 2 positive 1-tiles. The resulting equation is x = 2. 3. 5x – 7 = 8 7 positive 1-tiles to each side to form zero pairs. Group the tiles to form zero pairs and remove the zero pairs. Separate the remaining tiles into 5 equal groups to match the 5 x-tiles. Each x-tile is paired with 3 positive 1-tiles. The resulting equation is x = 3. 4. –7 = 3x + 8 SOLUTION: SOLUTION: 1 1 2 2 3 4 5 Place 5 x-tiles and 7 negative 1-tiles on one side of the mat. Place 8 positive 1-tiles on the other side. Since there are 7 negative 1-tiles with the x-tiles, add 7 positive 1-tiles to each side to form zero pairs. Group the tiles to form zero pairs and remove the zero pairs. Separate the remaining tiles into 5 equal groups to match the 5 x-tiles. Each x-tile is paired with 3 positive 1-tiles. The resulting equation is x = 3. 4. –7 = 3x + 8 4 Place 7 negative 1-tiles on one side of the mat. Place 3 x-tiles and 8 positive 1-tiles on the other side. Since there are 8 positive 1-tiles with the x-tiles, add 8 negative 1-tiles to each side to form zero pairs. Group the tiles to form zero pairs and remove the zero pairs. Separate the remaining tiles into 3 equal groups to match the 3 x-tiles. Each x-tile is paired with 5 negative 1-tiles. The resulting equation is x = – 5. 5. 5 + 4x = –11 SOLUTION: SOLUTION: 1 eSolutions Manual - Powered by Cognero 1 Page 2 Group the tiles to form zero pairs and remove the zero pairs. Separate the remaining tiles into 3 equal groups to match the 3 x-tiles. Each x-tile is paired with 2-3: 5 negative 1-tiles. resulting equation Equations is x = – Explore Algebra LabThe Solving Multi-Step 5. 5. 5 + 4x = –11 Group the tiles to form zero pairs and remove the zero pairs. Separate the remaining tiles into 4 equal groups to match the 4 x-tiles. Each x-tile is paired with 4 negative 1-tiles. The resulting equation is x = – 4. 6. 3x + 1 = 7 SOLUTION: SOLUTION: 1 1 2 2 3 4 3 Place 3 x-tiles and 1 positive 1-tile on one side of the mat. Place 7 positive 1-tiles on the other side. Remove 1 positive 1-tile from each side. Separate the remaining tiles into 3 equal groups to match the 3 x-tiles. Each x-tile is paired with 2 positive 1-tiles. The resulting equation is x = 2. 7. 11 = 2x – 5 4 Place 4 x-tiles and 5 positive 1-tiles on one side of the mat. Place 11 negative 1-tiles on the other side. Since there are 5 positive 1-tiles with the x-tiles, add 5 negative 1-tiles to each side to form zero pairs. Group the tiles to form zero pairs and remove the zero pairs. Separate the remaining tiles into 4 equal groups to match the 4 x-tiles. Each x-tile is paired with 4 negative 1-tiles. The resulting equation is x = – 4. 6. 3x + 1 = 7 SOLUTION: 1 2 SOLUTION: 1 3 eSolutions Manual - Powered by Cognero Page 3 mat. Place 7 positive 1-tiles on the other side. Remove 1 positive 1-tile from each side. Separate the remaining tiles into 3 equal groups to match the 3 x-tiles. Each x-tile isLab paired with 2Multi-Step positive 1-tiles. Explore 2-3: Algebra Solving Equations The resulting equation is x = 2. 7. 11 = 2x – 5 tiles with the x-tiles, add 5 positive 1-tiles to each side to form zero pairs. Grou form zero pairs and remove the zero pairs. Separate t tiles into 2 equal groups to match the 2 x-tiles. Each x with 8 positive 1-tiles. The resulting equation is x = 8. 8. 7 + 6x = –11 SOLUTION: SOLUTION: 1 1 2 3 2 4 Place 11 positive 1-tiles on one side of the mat. Place 5 negative 1-tiles on the other side. Since there are 5 tiles with the x-tiles, add 5 positive 1-tiles to each side to form zero pairs. Grou form zero pairs and remove the zero pairs. Separate t tiles into 2 equal groups to match the 2 x-tiles. Each x with 8 positive 1-tiles. The resulting equation is x = 8. 3 8. 7 + 6x = –11 SOLUTION: 4 Place 6 x-tiles and 7 positive 1-tiles on one side of th mat. Place 11 negative 1-tiles on the other side. Sinc there are 7 positive 1-tiles with the x-tiles, add 7 nega 1-tiles to each side to form zero pairs. Group the tiles form zero pairs and remove the zero pairs. Separate t remaining tiles into 6 equal groups to match the 6 x-til Each x-tile is paired with 3 negative 1-tiles. The resul equation is x = –3. 1 9. What would be your first step in solving 8x – 29 = 67? eSolutions Manual - Powered by Cognero Page 4 SOLUTION: To solve 8x – 29 = 67, we need to isolate the x term on the left side. To do this, we would add 29 to each 1-tiles to each side to form zero pairs. Group the tiles form zero pairs and remove the zero pairs. Separate t remaining tiles into 6 equal groups to match the 6 x-til Explore Multi-Step Equations Each2-3: x-tileAlgebra is pairedLab withSolving 3 negative 1-tiles. The resul equation is x = –3. 9. What would be your first step in solving 8x – 29 = 67? SOLUTION: To solve 8x – 29 = 67, we need to isolate the x term on the left side. To do this, we would add 29 to each side. Using algebra tiles, add 29 yellow 1-tiles to each side. 10. What steps would you use to solve 9x + 14 = –49? SOLUTION: To solve 9x + 14 = –49, first we need to isolate the x-term on the left side. To do this, subtract 14 from each side. Using algebra tiles, add 14 red –1-tiles to each side. This leaves 9x = –63. Then, divide each side by 9. Using algebra tiles, group each x-tile with 7 red –1-tiles. eSolutions Manual - Powered by Cognero Page 5