1. -3 - 3 Objective - To solve equations with the variable in both sides. Solve. 2x + 4 = 5x - 17 -2x 4 = 3x - 17 +17 21 = 3x 3 7 = x -5x -3x + 4 = -17 -4 -3x = -21 x = 7

2. 1) Goal: Isolate the variable. 2) Undo operations with their opposite operation. 3) Always do the same thing to both sides of the equation. 4) Easiest to undo add/subtract before multiply/divide.

3. 1) Goal: Isolate the variable on one side of the equation. 4) Easiest to undo add/subtract before multiply/divide. 2) Undo operations with their opposite operation. 3) Always do the same thing to both sides of the equation.

4. Solve. 1) 4(x - 2) - 2x = 5(x - 3) 4x - 8 - 2x = 5x - 15 2x - 8 = 5x - 15 -2x -8 = 3x - 15 +15 7 = 3x 3

5. 2) 3(x + 2) - (2x - 4) = - (4x + 1) 3x + 6 - 2x + 4 = - 4x - 1 x + 10 = - 4x - 1 + 4x 5x + 10 = -1 - 10 -10 5x = -11 5 x = =

6. 3) 5(m - 6) = 10 - 4[2(m - 7) - 5m] 5m - 30 = 10 - 4[2m - 14 - 5m] 5m - 30 = 10 - 4[-3m - 14] 5m - 30 = 10 + 12m + 56 5m - 30 = 12m + 66 -5m -30 = 7m + 66 -66 -96 = 7m 7

7. Solve each equation below. a) 3x - 5 = 2x + 12 b) 3x + 8 = 2(x + 4) + x c) 3x + 2 = 2(x - 1) + x -2x x - 5 = 12 +5 x = 17 3x + 8 = 2x + 8 + x 3x + 8 = 3x + 8 -3x 8 = 8 3x + 2 = 2x - 2 + x 3x + 2 = 3x - 2 -3x 2 = -2 One Solution Identity x = any real number True ! False ! No Solution

8. Solve. 4) 4(y - 2) + 6y = 7(y - 8) - 3(10 - y) 4y - 8 + 6y = 7y - 56 - 30 + 3y 10y - 8 = 10y - 86 -10y -8 = -86 False Statement No Solution

9. Solve. 5) 3(4 + k) - 2(3k + 4) = 5(k - 3) - (8k - 19) 12 + 3k - 6k - 8 = 5k - 15 - 8k + 19 -3k + 4 = -3k + 4 +3k 4 = 4 True Statement Infinitely Many Solutions x = any real number

10. Use a variable equation to solve. 4) Find a number that is 20 more than 4 times its opposite. Let x = the number -x = the opposite x = 4(-x) + 20 x = -4x + 20 +4x 5x = 20 5 x = 4