1. Lesson 3.3 Solving Equations with Variables on Both Sides
Essential Question: How do you solve equations with variables on both sides?

2. Before we start…
David has $26 and saves $8 each week. Emily has $56 and saves $4 each week. How many weeks will it take for David and Emily to have the same amount of money?

3. Variables on Both Sides of the Equation
Continue to use inverse operations to isolate the variable.
Collect variable terms on side and constant terms on the other side

4. How do I solve an equation with variables on both sides?
Simplify expressions on both sides of the equation.
Collect all variable terms on one side of the equation.
Collect all constant terms on the other side of the equation.
Use inverse operations to isolate the variable.

5. Solve 7𝑛−5=10𝑛+13

6. Solve 5𝑛−2=3𝑛+6

7. Solve 8𝑦+4=11𝑦−17

8. Solve 𝑚−1=9𝑚+15

9. Solve 5 2𝑥+1 =10𝑥

10. Solve 6𝑥+2=2 3𝑥+1

11. Solve 3𝑥−7=8+6 𝑥+2

12. Solve 13𝑦+19=6 9+𝑦 +14

13. Solve 8 𝑧+4 =5 13+𝑧

14. Solve 8𝑎−2 𝑎+5 =2 𝑎−1

15. Solve 4 −2+3𝑥 =12𝑥

16. Solve 7 2𝑥+3 =21+14𝑥

17. Spanish Club The Spanish club is arranging a trip to a Mexican restaurant in a nearby city. Those who go must share the $60 cost of using a school bus for the trip. The restaurant’s buffet costs $5 per person. How many students must sign up for this trip in order to limit the cost to $10 per student?

18. Tour Bus A bus tour of celebrities’ homes costs $300 for the bus and tour guide plus $8 per person for lunch. How many people does a tour group need to have in it so that the cost per person is $20?

19. Shopping You spend $60 on clothes and buy 3 DVD movies
Shopping You spend $60 on clothes and buy 3 DVD movies. Your friend spends nothing on clothes and buys 8 DVD movies. You both spend the same amount of money. All the DVDs cost the same amount. How much does each DVD cost?

20. How do you solve equations with variables on both sides?

21. Ticket Out the Door
Solve
2𝑥−6=4 5𝑥+12