One, None, and Infinite Solutions

One, None, and Infinite Solutions

by Lisa Lerma

​What do you notice and wonder?

​Timed Pair Share

Open Ended

What do you notice and wonder?

​One Solution

Equations that have exactly one solution.

Multiple Choice

Solve for x.

• x = 3

• x = 6

• x = -2

• x = -5

Draw

Solve for n. Show all your work.

Multiple Choice

• v = 15

• v = 3

• v = 24

• v = 33

Multiple Choice

• r = 6

• r = 7

• r = -6

• r = 13

Draw

Solve for k. Show all your work.

2x + 3 = 2x + 7

Multiple Choice

How many x's can we remove from both sides of the equation 2x + 3 = 2x + 7?

• 1 from each side of the equation.

• 4 from each side of the equation.

• 2 from each side of the equation.

• None

Multiple Choice

What is you new equation after removing 2x from each side?

• 2x + 3 = 4x + 2

• 3 = 7

• 2x + 3 = 7

• 3 = 2x + 7

Open Ended

Since we simplify down to 3 = 7 as our equation, what can we say is our solution to the equation? Explain.

​No Solutions

​Equations that have no solutions. No values we assign to the variable will make the equation true.

Multiple Choice

What should be my first step to solve the equation?

• Subtract 2x from both sides.

• Subtract 6 and add 2x to both sides.

• Add 6 to both sides.

• Distribute -2 by multiplying it to x and +3.

What would be our solution? Explain.

Open Ended

What would be our solution? Explain.

​Infinite Solutions

There is an infinite amount of solutions to the equation. Any value ​for the variable would make the equation true.

Multiple Choice

How many solutions are there in the following equation?

• one

• no solutions

• infinite solutions

Multiple Choice

How many solutions are there in the following equation?

• one

• no solutions

• infinite solutions

Multiple Choice

How many solutions are there in the following equation?

• one

• no solutions

• infinite solutions

Multiple Choice

How many solutions are there in the following equation?

• one

• no solutions

• Infinite solutions

Open Ended

Describe the differences with equations that have one, none, or infinite solutions?