Type of Equation Solutions

Type of Equation Solutions

I can classify equations by their solution.

Criteria for Success

• Understand that if an equation has no solution, then there is no value for x that will make the equation true

• Understand that if an equation has infinite solutions, then x can represent any value and it will make the equation true

• Understand that if an equation has a unique solution, then there is one value for x that will make the equation true

Do Now

Don’t try to solve.  Just looking at this equation- What’s wrong with this?

 $x+2=x+3$  

Picture This:

These scales are all currently balanced. You must choose a number to fill into the boxes in each problem that will keep them balanced. In each individual box you may only use one number.

Picture This:

These scales are all currently balanced. You must choose a number to fill into the boxes in each problem that will keep them balanced. In each individual box you may only use one number.

Picture This:

These scales are all currently balanced. You must choose a number to fill into the boxes in each problem that will keep them balanced. In each individual box you may only use one number.

Open Ended

You must choose a number to fill into the boxes in each problem that will keep them balanced. In each individual box you may only use one number.

Open Ended

You must choose a number to fill into the boxes in each problem that will keep them balanced. In each individual box you may only use one number.

Open Ended

You must choose a number to fill into the boxes in each problem that will keep them balanced. In each individual box you may only use one number.

Types of Solutions

• One Solution Equations

• Infinite Solutions

• No Solution

One Solution

Variable Terms: On one side or different

Constants: Same or different

Infinite Solution

Variable Terms: Same

Constants: Same

No Solution

Variable Terms: Same

Constants: Different

Practice

Multiple Choice

 $7x-3=7x+5$  

• No Solution

• Infinite Solutions

•  $x=2$  

•  $x=8$  

Multiple Choice

Determine the type of solution you will have if you get
x=0.25

• one solution
• infinite solution=identity
• no solution
• I don't know.  I need to study.

Multiple Choice

How many solutions to this equation????  3 (10x + 2) = 30x + 6

• One Solution
• No Solution
• Infinite Solutions

Multiple Choice

3r - 5 = 2r

• No solution
• Infinitely many solutions
• r = 5

Multiple Choice

Solve:
2x + 1 = 2x - 1

• No Solution
• x = 0
• Infinitely Many Solutions

Multiple Choice

Identify the type of solution.

• Infinite solutions

• One solution

• No solution

Multiple Choice

What is the solution to the equations?

• one solution
• no solution
• infinite solutions
• none of these

Multiple Choice

What is the solution to this equation?

• one solution

• no solution

• infinite solutions

• none of these

Exit Ticket

Open Ended

Todd and Jason both solved an equation and ended up with this final line in their work:

−2x=4x.

Todd says, “This equation has no solution because −2≠4.”

Jason says, “The solution is −2 because −2(−2)=4.”