Number of Solutions to Equations

Create Equations for a Certain Number of Solutions

One Solution, No Solutions, Infinite Solutions

One solution

• Means that only one number can make the statement true

• Solutions shown as: x=3, y=8, b=4, x = -5

• A way to tell if the equation only has one solutions is that there are a different amount of x's on each side

• For example: 4x = 6x or 5x+3= 8x+6

No solution

• Means that NO number you choose can make the statement true

• Solutions look like: 3=5 or -4 = 9 or 2 = -32

• A way to tell if the equation is NO solution is that there are the same amount of x's on each side but the constants are different on each side

• For Example: 3x +4 = 3x -5 or 6x - 4 = 6x + 10

Infinite (All) Solutions

• Means that no matter what number you give me it WILL be a solution to the equation

• Solutions look like: 2 = 2 or 4=4 or -3 = -3 or 0 = 0

• A way to tell if the equation is ALL solutions is that there are the SAME amount of x's on each side and there are the SAME amount of constants on each side.

• For example: 4x + 5 = 4x + 5 or 2x - 3 = 2x -3

Multiple Choice

What is the solution to this equation?

• One solution

• No solution

• Infinite (All) Solutions

Multiple Choice

What is the solution to the equations?

• One Solution

• No Solution

• Infinite Solutions

Multiple Select

What number do I need to be able to have INFINITE solutions? 3 = _

• 0

• - 3

• 6

• 3

Multiple Choice

How many solutions does this equation have?

6x + 9 = 3x + 9

• One Solution

• No Solution

• Infinite (All) Solutions

• I am confused

Multiple Select

What is the missing number that would make the equation true for NO solution?

3x + 5 = 3x + _

• 0

• -5

• 5

• 7

Multiple Select

What is the missing number that would make the equation true for ONE solution?

(Select all that apply)

4x + 5 = _ - 6

• 4x

• 3x

• 10x

• 5x

Open Ended

What is the missing information that would make the statement true for INFINITE solutions?

_ + 10 = 5x + 10