Unit 4 Lesson 8: How Many Solutions?

Unit 4 Lesson 8: How Many Solutions?

Multiple Choice

Consider the unfinished equation 12(x-3) + 18 = ___. Match the following expressions with the number of solutions the equation would have with that expression on the right hand side.

6(2x-3)

• One solution?

• No solutions?

• All Solutions?

Multiple Choice

Consider the unfinished equation 12(x-3) + 18 = ___. Match the following expressions with the number of solutions the equation would have with that expression on the right hand side.

4(3x-3)

• One solution?

• No solutions?

• All Solutions?

Multiple Choice

Consider the unfinished equation 12(x-3) + 18 = ___. Match the following expressions with the number of solutions the equation would have with that expression on the right hand side.

4(2x-3)

• One solution?

• No solutions?

• All Solutions?

Activity Synthesis

• What do you notice about equations with no solution?

• What do you notice about equations that are always true?

• What do you notice about equations that have exactly one solution?

One, None, or Infinite

What do you see that will help decide?

One, None, or Infinite

What do you see that will help decide?

One, None, or Infinite

What do you see that will help decide?

One, none, infinite

• What do you notice about equations with one solution?

• How is this different from equations with no solutions and equations that are true for every x ?

Lesson Synthesis

“What do you notice about equations with one solution?”

“What do you notice about equations with no solutions?”

“What do you notice about equations with infinitely many solutions?”