Topic: Infinite and No Solution Equations

Topic: Infinite and No Solution Equations

Essential Questions

• What are the different types of solutions for the equations? 

• What does it mean when an equation has no solution? 

• What does it mean when an equation has infinite solutions? 

Open Ended

What do you think that one-solution means?

Open Ended

What do you think that no solution means?

Solve the following equation

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Solve the following Equation

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Open Ended

What are some things that you notice that are similar in each of these equations?What are somethings that you notice that are different?

Open Ended

What do you think infinite solutions mean?

Solve the following equation.

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Solve the following equation

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Open Ended

What are some things that you notice that are similar in each of these equations?What are somethings that you notice that are different?

An equation has NO SOLUTION when:

• An equation is in the form ax+b = ax+b (You have variables on both sides and you have distributed and combined like terms)

• The coefficient of x is the SAME

• The constant is DIFFERENT

An equation has INFINITE SOLUTIONS(Identity)

• An equation is in the form ax+b = ax+b (You have variables on both sides and you have distributed and combined like terms)

• The coefficient of x is the SAME

• The constant of x is the SAME

Let's do a few examples!

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Multiple Choice

How many solutions does the following equation have?

 $2x\ +\ 2x+\ 2=\ 4x\ +\ 2$  

• One Solution

• No Solution

• Infinite Solution

Multiple Choice

How many solutions does the following equations have?

 $3\left(x-1\right)=\ 2x\ +\ 9$  

• One Solution

• No Solution

• Infinite Solutions

Multiple Choice

How many solutions does the following equations have?

 $2x\ +\ 8\ =\ 2\left(x\ +\ 4\right)$  

• One Solution

• No Solution

• Infinite Solutions

Multiple Choice

How many solutions does the following equations have?

 $-2\left(x\ +\ 1\right)=-2x\ +\ 5$  

• One Solution

• No Solution

• Infinite Solution

Multiple Choice

How many solutions does the following equations have?

 $4\left(x-1\right)=\ \frac{1}{2}\left(x\ -\ 8\right)$  

• One Solution

• No Solution

• Infinite Solutions

Multiple Choice

How many solutions does the following equations have?

 $x+\ 2x\ +\ 7\ =\ 3x\ -\ 7$  

• One Solution

• No Solution

• Infinite Solutions