1. GOAL 1 COLLECTING VARIABLES ON ONE SIDE 3.4 Solving Equations with Variables on Both Sides EXAMPLE 1EXAMPLE 2 The technique: Find the variable with the largest coefficient, and collect its like terms on that side of the equation.

2. Extra Example 1 Click to see the solution

3. Extra Example 2 EXAMPLE 3 Some equations have infinitely many solutions and are called identities, and some equations have no solutions. Click to see the solution

4. Extra Example 3 a. Solve Click to see the solution

5. Extra Example 3 b. Solve EXAMPLE 4 Click to see the solution

6. Extra Example 4 Click to see the solution

7. Extra Example 4 (cont.) Click to see the solution

8. Checkpoint

9. Checkpoint (cont.)

10. GOAL 2 SOLVING REAL-LIFE PROBLEMS EXAMPLE 5 3.4 Solving Equations with Variables on Both Sides

11. Extra Example 5 A gym offers two packages for yearly membership. The first plan costs $50 to be a member. Then each visit to the gym is $5. The second plan costs $200 for a membership fee plus $2 per visit. Which membership is more economical? Hint: Find the number of visits for which the two plans will cost the same. Click to see the solution

12. Checkpoint One CD music club charges a $30 membership fee plus $10 per CD. Another club charges $15 per CD but has no membership fee. Which club is more economical? The cost is the same for 6 CDs. If more than 6 are purchased, the club with the $30 membership fee is more economical. If fewer than 6 are purchased, the club without a membership fee is more economical.

13. QUESTIONS?