1. 3.4 Solving Equations with Variables on Both Sides Objective: Solve equations that have variables on both sides.

2. What do we do when variables appear on both sides of the equation?

3. Equations with Variables on Both Sides Some equations have variables on both sides To solve these equations, you can first collect the variable terms on one side of the equation Collecting the variable terms on the side with the greater variable coefficient will result in a positive coefficient

4. Solve 7x + 19 = -2x + 55 30 – 9y = 6y

5. Solve 34 – 3x = 14x 5y – 2 = y + 10

6. Solve -6x + 4 = -8x 3x – 10 + 4x = 5x – 7

7. Solve 5x – 3x + 4 = 3x + 8 6x + 3 = 8 + 7x + 2x

8. Number of Solutions So far you have seen linear equations that have only one solution. Some linear equations have no solution. No solution occurs when you end up with a false statement 6 ≠ 4 An identity is an equation that is true for all values of the variable. An identity has infinitely many solutions. Infinitely many solutions occur when you a get a number equal to itself 6 = 6

9. Solve the equation and determine how many solutions it has. 3(x + 2) = 3x + 6 3(x + 2) = 3x + 4 3(x + 2) = 2x + 4

10. Solve the equation if possible and determine the number of solutions. 2(x + 4) = 2x + 8 2( x + 4) = x - 8

11. Solve the equation if possible and determine the number of solutions. 2(x + 4) = 2x – 8 2(x + 4) = x + 8