1. Objective - To solve multi-step variable equations including word problems. Chapter 2-2September 24, 2008 Solving Multi-Step Equations

2. Goal: Isolate the variable. 1._______________________________________ _______________________________________ 2._______________________________________ _______________________________________ 3._______________________________________ _______________________________________ Draw a vertical line at = sign to separate two sides of equation. (ALWAYS line up = signs.) Use distributive property to rid equation of any expressions within parentheses. Combine all like terms on each side of equation. Rewrite new equation.

3. Solve. 1) 3(x - 2) = 17 2) - (5 - x) = 9 = 17 +6 3x = 23 3 = 9 +5 x = 14 1 3x- 6-5-5+ x

4. Solve. 3) 12 - 2(x + 4) = 28 12 = 28 -2x = 28 -4 -2x = 24 -2 x = -12 - 2x- 8 + 4

5. Solve. 4) 6(x + 4) - 2(x - 7) = 10 6x + 24 - 2x + 14 = 10 4x + 38 = 10 -38 4x = -28 4 x = -7

6. Problem Solving Using Models Problem Solving Plan Relate Define Write Algebraic Model Solution State The answer

7. You want two rectangular gardens to have equal areas. The First garden is 5 meters by 16 meters. The second garden Is 8 meters wide. How long should the second garden be? 1. Length of 1 st garden = Length of 1 st garden Width of 1 st garden Length of 2 nd garden Width of 2 nd garden 16 meters (16)(5) = x(8) The second garden should be 10 m long. Relate: Width of 1 st garden Length of 2 nd garden Width of 2 nd garden Define: = = = = 5 meters x 8 meters Algebraic Model: Solution: x = 10 Answer: 16 5 x8 80 = 8x

8. You and your friends went to a music store to buy CD’s on sale for $6 each. Together you spent $77.76, which included a tax of $5.76. Use modeling to find how many CD’s you bought together. 2. Number of CD’s bought = n(6) + 5.76 = 77.76 You and your friends bought 12 CD’s. Relate: Cost per CD Tax amount Total Spent Algebraic Model: Solution: n = 12 Answer: + n 6 5.76 77.76 - 5.76 6n = 72.00 6

9. Trick for solving problems with fractions: To get rid of fractions: 1. Find the LCD of all denominators. 2. Multiply EACH TERM by this LCD. 3. Now solve new equation.