Objective

• To solve equations with variables on both sides

• To identify equations that are identities or have no solution

Remember

Our goal in solving an equation is to isolate the variable (we want it to look like x = some number). We have two tools we can use:

• Inverse operations ("undo")

• Properties of equality ("both sides")

But what if there are variables on both sides of the equation?

Like such:

Turns out, you get to pick

Example

Example

Example

Break-even problems

Shirley is going to have the exterior of her home painted. Tim’s painting charges $250 plus $14 per hour. Colorful Paints charges $122 per hour. How many hours would the job need to take for Tim’s Painting to be the better deal?

​Colorful Paints

​Tim's Painting

Break-even problems

Break-even Problems

​So Tim's Painting is a better deal for a job that takes three or more hours.

Identities/No Solution

​12 = 12 is obviously true, but there's no variable. This means the equation is true no matter what value we use for x. This kind of equation is called an identity.

Identities/No Solution

x = a number (One solution)

a number equals itself (Identity)

a number equals some other number (No solution)