1. Solve Equations with Variable on Each Side (10-5)

2. Warm-Up
You and your friend are having a race. You give your friend a 15-minute head start. During the race, you average 6 meters per second, and your friend average 5 meters per second.
Time (s)
Friend’s Distance (m)
Your Distance (m)
15 + 5(0) = 15
6(0) = 0 1
15 + 5(1) = 20
6(1) = 6 2
15 + 5(2) = 25
6(2) = 12 3
15 + 5(3) = 30
6(3) = 18 …
1. Copy the table. Continue filling in rows to find how long it will take you to catch up to your friend.
2. Write an expression for your distance after seconds.
3. Write an expression for your friend’s distance after seconds.
4. Are the distances you and your friend have gone when you catch up to your friend the same or different?
5. Write an equation that could be used to find how long it will take for you to catch up to your friend.

3. Steps to Solving
1. Keep – Change – Change 2. Move the variables so they are on the same side. **Hint: Think about whether the resulting coefficient will be positive or negative, and try to move them so the coefficient is positive! 3. Simplify the side with the variable by combining like terms. 4. Solve the resulting 1- or 2- Step Equation.

4. Example #1 Write the equation Keep – Change – Change
Move the variables
Solve the equation

5. Example #2 Write the equation Move the variables Solve the equation
Keep – Change – Change (n/a)
Move the variables
Solve the equation

6. Example #3 Write the equation Keep – Change – Change
Move the variables
Solve the equation

7. Example #4 Write the equation Keep – Change – Change
Move the variables
Solve the equation

8. Word Problem Example #1
EZ Car Rental charges $40 a day plus $0.25 per mile. Ace Rent-A-Car charges $25 a day plus $0.45 per mile. Write an equation to find the number of miles results in the same cost for one day.
EZ Car Rental = Ace Rent-A-Car

9. Word Problem Example #2
For an annual membership fee of $30, you can join a movie club that will allow you to purchase tickets for $5.50 each at your local theater. The theater in your area charges $8 for movie tickets. Write an equation you can use to determine the number of movie tickets you need to buy through the movie club for the cost to equal that of buying tickets at the regular price.
Movie Club = Regular Price

10. Geometry Example
Write an equation to find the value of x so that each pair of polygons has the same perimeter.