3-5 Solving Equations with the Variable on Each Side

• Objectives• SWBAT:• 1) solve equations with the variable on each

side• 2) solve equations involving grouping symbols• 3) solve equations with one solution, no

solutions, and infinite solutions

1) Distribute first is possible2) Combine like terms on the same side of the equal sign3) Bring variable terms to one side of the equal sign. Bring constants to the other.Solve using INVERSE operations

Example 1:

Example 2:

Example 3:

Try these:

a) After how many visits are the two plans the same price?

b) After how many visits would it be cheaper to become a member?

Example: A health club has two payment plans. You can become a member by paying a $10 new member fee and use the gym for $5 a visit. Or, you can use the gym as a nonmember for $7 a visit. Compare the costs of the two payment plans.

Try:A video store charges $8 to rent a video game for five days. Membership to the video store is free. A video game club charges only $3 to rent a game for five days, but membership in the club is $50 per year. Compare the costs of the two rental plans.

a) After how many rentals are the two plans the same price?

b) After how many rentals would it be cheaper to become a member?

Solve :

Depending on how far you went simplifying you may have:

Or

Or

When the left side is identical to the right side like above, our solution is

ALL REAL NUMBERS

Solve:

Try:

1) 2)

3) 4)

John and Jeremy Ryan drove from Buffalo to Syracuse at an average rate of 48 miles per hour. On the return trip along the same road they were able to travel at an average rate of 60 miles per hour. The trip from Buffalo to Syracuse took one-half hour longer than the return trip. How long did the return trip take?

A cheetah running 90 feet per second is 100 feet behind a gazelle running 70 feet per second. How long will it take the cheetah to catch up to the gazelle? Write and solve a linear equation.